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SEO Keyword summary for en.wikipedia.org/wiki/continuous_probability_distribution
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be probability
Focus keyword
Short and long tail
Short Tail Keywords probability distribution displaystyle |
long Tail Keywords (2 words) probability distribution probability distributions random variable sample space cumulative distribution |
long Tail Keywords (3 words) cumulative distribution function probability density function absolutely continuous probability continuous probability distribution move to sidebar probability mass function continuous probability distributions |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/continuous_probability_distribution page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
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probability distribution wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
wikipedia free encyclopedia displaystyle omega tfrac ptext textptext texttfrac boldsymbol mathcal pxx infty pcolon ato mathbb subseteq pxin egeq forall ein eleq bigcup ieisum ipxin xmathcal esubset axb pxxq fxpxleq leq fxleq lim xto praxleq bfbfa fmathbb esum acap epxomega pxpxx pntfrac dots xsum xpomega delta apomega pxsum fxsum xomega eint efxdxsum int edelta sum epomega uiomega uii pleftbigcup iomega irightsum ipomega isum ipxui iui iabsubset pleftaleq xleq brightint abfxdx aleq aint afxdx xint xftdt mid xmathbb gamma abrightarrow sint trightarrow xbegincases textif ugeq pendcases prx pruppquad prugeq fmathit inv uleq fxfmathit invuleq elambda beginalignedfxuleftrightarrow ptleftrightarrow lambda xln xfrac uendaligned invufrac xfmathit textstyle paleq btint abdxpsi icon edit wikidata wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/continuous_probability_distribution
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Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
continuous found in path !
distribution found in path !
probability found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
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Navigation and internal links
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Human readable urls
Number of links
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statistics
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w httpsenwikipediaorgwindexphptitleprobabilitydistributionoldid1240645824absolutelycontinuousprobabilitydistribution
page information
printable version
continuous probability distribution
physica medica
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wiki distribution
statistics
probability theory
probability
kolmogorovs probability axioms
determinism
system
indeterminism
random
probability space
sample space
collectively exhaustive events
elementary event
mutual exclusivity
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bernoulli trial
bernoulli
binomial
exponential
normal gaussian
pareto
poisson
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random variable
bernoulli process
continuous or discrete
mean
variance
markov chain
observed value
random walk
stochastic process
complementary event
multivariate joint
marginal probability
conditional probability
independence
conditional independence
law of total probability
law of large numbers
bayes theorem
booles inequality
venn diagram
tree diagram
function
subsets
the coin is fair
real numbers
vectors
random variables
probability mass function
dice
g
probability density function
infinitesimal
integrating
cumulative distribution function
algebra
real number
kolmogorov axioms
discrete
stochastic processes
continuous time
univariate
vector space
multivariate distributions
random vector
hypergeometric
moment generating function
characteristic function
quantile function
frequency distribution
relative frequency
sample
categorical
support
weighted average
median
mode
quantile
dispersion
standard deviation
symmetry
skewness
standardized moment
kurtosis
rightcontinuous
mixture
absolutely continuous
singular continuous distribution
convex sum
almost surely
countably infinite
geometric
negative binomial
empirical distribution
discrete uniform distribution
jump discontinuities
dirac measures
degenerate
dirac delta function
generalized
disjoint sets
deterministic distribution
absolutely continuous
integral
chisquared
absolutely continuous
singular
cantor
absolutely continuous
absolutely continuous measure
measuretheoretic
measurable function
measurable space
image measure
rabinovichfabrikant equations
hypercubes
balls
system of differential equations
langmuir waves
plasma
dynamical systems
ergodic theory
pseudorandom number sampling
pseudorandom number generator
halfopen interval
random variates
monte carlo method
pseudorandom numbers
kinetic properties of gases
quantum mechanical
fundamental particles
numbers
lognormal
power law
discrete uniform
uniform
independent
sampling without replacement
betabinomial
plya urn model
multinomial
multivariate hypergeometric distribution
gamma
rayleigh
rice
rician fading
standard normal
sample variance
chisquared
students t distribution
chi squared
mean
students ttest
rsquared
pearson productmoment
conjugate prior
beta
precision
dirichlet
wishart
nonnegative definite
covariance matrix
cache language models
statistical language models
natural language processing
wavefunction
born rule
triple integral
powerflow study
tropical cyclones
probability distribution fitting
predict
forecast
frequency
conditional probability distribution
empirical probability distribution
histogram
quasiprobability distribution
riemannstieltjes integral application to probability theory
list of statistical topics
isbn
oclc
s2cid
heavytailed distribution
longtailed distribution
fattailed distribution
lebesgues decomposition theorem
issn
bibcode
pmid
encyclopedia of mathematics
ems press
benford
poisson binomial
rademacher
soliton
zipf
zipfmandelbrot
beta negative binomial
borel
conwaymaxwellpoisson
discrete phasetype
delaporte
extended negative binomial
floryschulz
gausskuzmin
logarithmic
mixed poisson
parabolic fractal
skellam
yulesimon
zeta
arcsine
argus
baldingnichols
bates
beta rectangular
continuous bernoulli
irwinhall
kumaraswamy
logitnormal
noncentral beta
pert
raised cosine
reciprocal
triangular
uquadratic
wigner semicircle
benini
benktander 1st kind
benktander 2nd kind
beta prime
burr
noncentral
dagum
davis
erlang
hyperexponential
hypoexponential
logarithmic
noncentral
folded normal
frchet
generalized
inverse
gammagompertz
gompertz
shifted
halflogistic
halfnormal
hotellings tsquared
inverse gaussian
generalized
kolmogorovsmirnov
logcauchy
loglaplace
loglogistic
logt
lomax
matrixexponential
maxwellboltzmann
maxwelljttner
mittagleffler
nakagami
phasetype
polyweibull
relativistic breitwigner
truncated normal
type2 gumbel
weibull
discrete
wilkss lambda
cauchy
generalized normal
fishers z
kaniadakis gaussian
gaussian q
generalized hyperbolic
geometric stable
gumbel
holtsmark
hyperbolic secant
johnsons su
landau
laplace
asymmetric
logistic
noncentral t
normalinverse gaussian
skew normal
slash
stable
students t
tracywidom
variancegamma
voigt
generalized chisquared
generalized extreme value
generalized pareto
marchenkopastur
kaniadakis exponential
kaniadakis gamma
kaniadakis weibull
kaniadakis logistic
kaniadakis erlang
qexponential
qgaussian
qweibull
shifted loglogistic
tukey lambda
rectified gaussian
dirichlet
negative
generalized
multivariate laplace
multivariate stable
multivariate t
normalgamma
matrixvalued
matrix normal
matrix t
matrix gamma
normal
inverse
normalinverse
complex
directional
circular uniform
univariate von mises
wrapped normal
wrapped cauchy
wrapped exponential
wrapped asymmetric laplace
wrapped lvy
kent
bivariate von mises
von misesfisher
bingham
circular
compound poisson
elliptical distributions
exponential families
natural exponential
locationscale family
maximum entropy
pearson
tweedie
wrapped
raw moment
central moment
lmoments
momentgenerating function
probabilitygenerating function
cumulant
combinant
outline
descriptive statistics
continuous data
center
arithmetic
arithmeticgeometric
contraharmonic
cubic
generalizedpower
geometric
harmonic
heronian
heinz
lehmer
average absolute deviation
coefficient of variation
interquartile range
percentile
range
central limit theorem
moments
count data
index of dispersion
contingency table
grouped data
correlation
partial correlation
pearson productmoment correlation
rank correlation
scatter plot
graphics
bar chart
biplot
box plot
control chart
correlogram
fan chart
forest plot
pie chart
qq plot
radar chart
run chart
stemandleaf display
violin plot
data collection
study design
effect size
missing data
optimal design
population
replication
sample size determination
statistic
statistical power
survey methodology
sampling
cluster
stratified
opinion poll
questionnaire
standard error
controlled experiments
blocking
factorial experiment
interaction
random assignment
randomized controlled trial
randomized experiment
scientific control
adaptive clinical trial
stochastic approximation
upanddown designs
observational studies
cohort study
crosssectional study
natural experiment
quasiexperiment
statistical inference
statistical theory
population
sampling distribution
order statistic
density estimation
statistical model
model specification
lp space
parameter
location
scale
shape
parametric tests
likelihood
monotone
completeness
sufficiency
plugin
bootstrap
optimal decision
loss function
efficiency
statistical distance
divergence
asymptotics
robustness
frequentist inference
point estimation
estimating equations
maximum likelihood
method of moments
mestimator
minimum distance
unbiased estimators
meanunbiased minimumvariance
raoblackwellization
lehmannscheff theorem
median unbiased
interval estimation
confidence interval
pivot
likelihood interval
prediction interval
tolerance interval
resampling
jackknife
testing hypotheses
1 2tails
power
uniformly most powerful test
permutation test
randomization test
multiple comparisons
likelihoodratio test
scorelagrange multiplier
wald
specific tests
ztest normal
ftest
goodness of fit
gtest
andersondarling
lilliefors
jarquebera
normality shapirowilk
model selection
cross validation
rank statistics
sign
sample median
signed rank wilcoxon
hodgeslehmann estimator
rank sum mannwhitney
nonparametric
analysis of variance anova anova
1way kruskalwallis
2way friedman
ordered alternative jonckheereterpstra
van der waerden test
bayesian inference
bayesian probability
prior
posterior
credible interval
bayes factor
bayesian estimator
maximum posterior estimator
regression analysis
confounding variable
coefficient of determination
errors and residuals
regression validation
mixed effects models
simultaneous equations models
multivariate adaptive regression splines mars
linear regression
simple linear regression
ordinary least squares
regression
bayesian regression
nonlinear regression
nonparametric
semiparametric
isotonic
robust
heteroscedasticity
homoscedasticity
generalized linear model
logistic bernoulli
binomial
loglinear model
partition of variance
analysis of covariance
degrees of freedom
categorical
multivariate
timeseries
survival
cohens kappa
graphical model
mcnemars test
cochranmantelhaenszel statistics
principal components
canonical correlation
discriminant analysis
cluster analysis
classification
structural equation model
factor analysis
decomposition
trend
stationarity
seasonal adjustment
exponential smoothing
cointegration
structural break
granger causality
dickeyfuller
johansen
qstatistic ljungbox
durbinwatson
breuschgodfrey
time domain
autocorrelation acf
partial pacf
crosscorrelation xcf
arma model
arima model boxjenkins
autoregressive conditional heteroskedasticity arch
vector autoregression var
frequency domain
spectral density estimation
fourier analysis
leastsquares spectral analysis
wavelet
whittle likelihood
survival function
kaplanmeier estimator product limit
proportional hazards models
accelerated failure time aft model
first hitting time
hazard function
nelsonaalen estimator
logrank test
applications
biostatistics
bioinformatics
clinical trials
studies
epidemiology
medical statistics
engineering statistics
chemometrics
methods engineering
probabilistic design
process
quality control
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system identification
social statistics
actuarial science
census
crime statistics
demography
econometrics
jurimetrics
national accounts
official statistics
population statistics
psychometrics
spatial statistics
cartography
environmental statistics
geographic information system
geostatistics
kriging
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SEO Advice for en.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 87% | A title should reflect the contents of a site. This site has a 67 % match | |
Title Length | 80% | Limit your title to anywhere between 40 and 70 characters. Your title was 37 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 30% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 930 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 7 folders above or in the first level of navigation. | |
Headings | 46% | Headers should reflect the contents of a site. This site has a 20 % match | |
Links | 8% | Link anchors should to some degree reflect the contents of a site. This site has a 4 % match | |
Image alt tags | 11% | Image alt tags should to some degree reflect the contents of a site. This site has a 4 % match | |
Bold and italic | 45% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 15 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 90% | 89.887640449438 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 7906 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 88.98% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 583 inline style declarations ( <a style="color:green">) with a size of 15588 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
en.wikipedia.org images and descriptions
127 images found at en.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
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https://wikimedia.org/api/rest_v1/media/math/render/svg/14567090e62b518e1b9a0b5329f25535813b090d height: height attribute not set width: width attribute not set description: {\displaystyle e\subset x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/617e7bf2f419fd8a31234ec2b0d5c9df00457025 height: height attribute not set width: width attribute not set description: {\displaystyle e\in {\mathcal {a}}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/standard_deviation_diagram.svg/250px-standard_deviation_diagram.svg.png height: 125 width: 250 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/89862747e88ca143e979241a9a243b5ef66ddc67 height: height attribute not set width: width attribute not set description: {\displaystyle e,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4 height: height attribute not set width: width attribute not set description: {\displaystyle x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d height: height attribute not set width: width attribute not set description: {\displaystyle q} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/79df0788e4852e22fca7287153bb3b600d957b57 height: height attribute not set width: width attribute not set description: {\displaystyle r_{x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/97c7781302bc4c8b617ad8b41c37e8138d8ccdbe height: height attribute not set width: width attribute not set description: {\displaystyle x>a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fecb9477a9ff7f055e5108754fe9388f0187fd33 height: height attribute not set width: width attribute not set description: {\displaystyle x |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d355c5d91dc6c206477bbc961ef58b3f96f9fbcd height: height attribute not set width: width attribute not set description: {\displaystyle a |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/594e1c2862665c4c4d402f7ba2d661c9834e5427 height: height attribute not set width: width attribute not set description: {\displaystyle p(x |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36 height: height attribute not set width: width attribute not set description: {\displaystyle p} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3331ebba17c8829de342ac6670a45db7d4bff379 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=p(x\leq x).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/71a82805d469cdfa7856c11d6ee756acd1dc7174 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9ef53c38d15aca9ca7b4dbd72dc7af69ac84e142 height: height attribute not set width: width attribute not set description: {\displaystyle 0\leq f(x)\leq 1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c44131eca7398617138fa5a7ef1ce878053c84ae height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{x\to -\infty }f(x)=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/393b43f01003d9b9b5aacc20f9913191029defd0 height: height attribute not set width: width attribute not set description: {\displaystyle \lim _{x\to \infty }f(x)=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8cd4cd12484aa3aec4ef24ee66a34edd9df105b1 height: height attribute not set width: width attribute not set description: {\displaystyle \pr(a |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d02d30fa7eb4c2cf6cb40779cb6d07e993f9dc9 height: height attribute not set width: width attribute not set description: {\displaystyle f:\mathbb {r} \to \mathbb {r} } |
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https://upload.wikimedia.org/wikipedia/commons/thumb/1/12/dice_distribution_%28bar%29.svg/250px-dice_distribution_%28bar%29.svg.png height: 188 width: 250 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7186ed5f087b7b8ebf58d72fb80af6c0890f1b47 height: height attribute not set width: width attribute not set description: {\displaystyle p(s)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2 height: height attribute not set width: width attribute not set description: {\displaystyle s} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/01c09b5bc67a4f236b8f56a3d367756fd6c3b4d8 height: height attribute not set width: width attribute not set description: {\displaystyle p(11)=2/36=1/18} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/959b12ce5c1a6f009398e9b0cef521b11b09c2d0 height: height attribute not set width: width attribute not set description: {\displaystyle p(x>9)=1/12+1/18+1/36=1/6} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/8/85/discrete_probability_distrib.svg/220px-discrete_probability_distrib.svg.png height: 104 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/fb/discrete_probability_distribution.svg/220px-discrete_probability_distribution.svg.png height: 77 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/e8/normal_probability_distribution.svg/220px-normal_probability_distribution.svg.png height: 77 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/64/mixed_probability_distribution.svg/220px-mixed_probability_distribution.svg.png height: 77 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2e4b5f636393e75c3da05692ee877b605c410d00 height: height attribute not set width: width attribute not set description: {\displaystyle p(x\in e)=\sum _{\omega \in a\cap e}p(x=\omega ),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3 height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/edb55065b605213a635fe1f65c0f254bddc07f16 height: height attribute not set width: width attribute not set description: {\displaystyle p(x\in a)=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6c10bc497aaa4a27e77898ff933aa91e8ffe7842 height: height attribute not set width: width attribute not set description: {\displaystyle p(x)=p(x=x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/33bb344a3238f16d574897cf77be95ef70ce218b height: height attribute not set width: width attribute not set description: {\displaystyle p(n)={\tfrac {1}{2^{n}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/94007d32129e7d62758916268a12b6108a5b6e0a height: height attribute not set width: width attribute not set description: {\displaystyle n=1,2,...} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7f2b11caa92398c7657837bf035267c49d94cb50 height: height attribute not set width: width attribute not set description: {\displaystyle 1/2+1/4+1/8+\dots =1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/16e61e7d0b60b2ad27c1b93764aa5108f25b4478 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=p(x\leq x)=\sum _{\omega \leq x}p(\omega ).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8 height: height attribute not set width: width attribute not set description: {\displaystyle \omega } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9c12edf03721c82d470149b2680d82847a1e33bc height: height attribute not set width: width attribute not set description: {\displaystyle \delta _{\omega }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6d8f0387ec1557fc8a0e822399776007f4604a87 height: height attribute not set width: width attribute not set description: {\displaystyle p(x\in e)=\sum _{\omega \in a}p(\omega )\delta _{\omega }(e),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9bb59e2d2574c15424a0a4721064c5e9f3e757b6 height: height attribute not set width: width attribute not set description: {\displaystyle p_{x}=\sum _{\omega \in a}p(\omega )\delta _{\omega }.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61 height: height attribute not set width: width attribute not set description: {\displaystyle f} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/595c7423a680e50ee38fe3271546db9680dbcab7 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=\sum _{\omega \in a}p(\omega )\delta (x-\omega ),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7a263146c1b012c2bcf164df7324d4c965e14d02 height: height attribute not set width: width attribute not set description: {\displaystyle p(x\in e)=\int _{e}f(x)\,dx=\sum _{\omega \in a}p(\omega )\int _{e}\delta (x-\omega )=\sum _{\omega \in a\cap e}p(\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2566d01f104ef084ea424b8b35c2534f7f902b height: height attribute not set width: width attribute not set description: {\displaystyle e.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7a05f796c20d85e2b84a4164131e97432e866bdb height: height attribute not set width: width attribute not set description: {\displaystyle u_{0},u_{1},\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f0287108e3beaae1852b7c7a9e59a6173210dd95 height: height attribute not set width: width attribute not set description: {\displaystyle \omega _{i}=x^{-1}(u_{i})=\{\omega :x(\omega )=u_{i}\},\,i=0,1,2,\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b28d1881d03b77a61862b122ca61fea15c848bd7 height: height attribute not set width: width attribute not set description: {\displaystyle p\left(\bigcup _{i}\omega _{i}\right)=\sum _{i}p(\omega _{i})=\sum _{i}p(x=u_{i})=1.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/70cde4c6d385274c329d32b86760b8aa720d61eb height: height attribute not set width: width attribute not set description: {\displaystyle x(\omega )=\sum _{i}u_{i}1_{\omega _{i}}(\omega )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d1a15eaa9285cd4654e86a76f3318c6ab2aad95d height: height attribute not set width: width attribute not set description: {\displaystyle 1_{a}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af5bd1f171b32c2fd6a859e5f68b52b72aa9d921 height: height attribute not set width: width attribute not set description: {\displaystyle p(x{=}x)=1.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f8544ec4fd60d201e49cacb3afd640e760798489 height: height attribute not set width: width attribute not set description: {\displaystyle f:\mathbb {r} \to [0,\infty ]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1cad8a9865c17ed0c40a9e3f5eb3fe4a18df765e height: height attribute not set width: width attribute not set description: {\displaystyle i=[a,b]\subset \mathbb {r} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f height: height attribute not set width: width attribute not set description: {\displaystyle i} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f27b1708f4353f5241e8cda627aaa332b9f1c0ab height: height attribute not set width: width attribute not set description: {\displaystyle p\left(a\leq x\leq b\right)=\int _{a}^{b}f(x)\,dx.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/009ba797370ba083b8325edb2d6335c4c2513d9e height: height attribute not set width: width attribute not set description: {\displaystyle a\leq x\leq a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935 height: height attribute not set width: width attribute not set description: {\displaystyle [a,b]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf51e0600ed04f039ec1b01c452206db22523384 height: height attribute not set width: width attribute not set description: {\displaystyle p(x\in a)=\int _{a}f(x)\,dx.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57 height: height attribute not set width: width attribute not set description: {\displaystyle f} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2e39a193583a5ffde1dbc1ad328b3012302c82f4 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=p(x\leq x)=\int _{-\infty }^{x}f(t)\,dt} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6bb8743f7565082ed1a9ee0490d9d71be82eafaa height: height attribute not set width: width attribute not set description: {\displaystyle (\omega ,{\mathcal {f}},\mathbb {p} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/478d656144cecc9f1e5bbd8c4a14d4dd7092b82c height: height attribute not set width: width attribute not set description: {\displaystyle ({\mathcal {x}},{\mathcal {a}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81bd1ff5385266f88263eaa39be4569558576f1f height: height attribute not set width: width attribute not set description: {\displaystyle \{\omega \in \omega \mid x(\omega )\in a\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/573bd8cb9f9bd7a93f23974b566e8122563b16e9 height: height attribute not set width: width attribute not set description: {\displaystyle x_{*}\mathbb {p} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ed71c56e3ffce179c691e19808e83186f02188b7 height: height attribute not set width: width attribute not set description: {\displaystyle x_{*}\mathbb {p} =\mathbb {p} x^{-1}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/rabinovich_fabrikant_2314.png/300px-rabinovich_fabrikant_2314.png height: 225 width: 300 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1bcd8908c9fa46eb979ef7b67d1bb65eb3692cbb height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {r} ^{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/17c589016c8f3ea30f528d9a1c6c5f6f67cfe0a0 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {n} ^{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/58e103c376cd9ea50b5c12c8f5398ded4d2a3577 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma :[a,b]\rightarrow \mathbb {r} ^{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {r} ^{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/98c79950cd68df63696c26a82b8bcf05ce78d576 height: height attribute not set width: width attribute not set description: {\displaystyle t_{1}\ll t_{2}\ll t_{3}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc height: height attribute not set width: width attribute not set description: {\displaystyle o} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6e35e13fa8221f864808f15cafa3d1467b5d78ce height: height attribute not set width: width attribute not set description: {\displaystyle [t_{1},t_{2}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/82eae695d40fda9d1b713787d35efa48d9a95478 height: height attribute not set width: width attribute not set description: {\displaystyle [t_{2},t_{3}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0eb63cccca21b1edef50f707888e3204ab5fda1a height: height attribute not set width: width attribute not set description: {\displaystyle \sin(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b543f76f961ec3f52d78fa3d72c3d87a521dd3a7 height: height attribute not set width: width attribute not set description: {\displaystyle t\rightarrow \infty } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025 height: height attribute not set width: width attribute not set description: {\displaystyle u} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ea074f5b36db6eff17f1aa84d73e30e3de12c4d6 height: height attribute not set width: width attribute not set description: {\displaystyle 0
|
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https://wikimedia.org/api/rest_v1/media/math/render/svg/71a1cc9754e3861243bd6e273fc171cc6fda008a height: height attribute not set width: width attribute not set description: {\displaystyle x={\begin{cases}1,&{\text{if }}u
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ea5c250e1de914d6e1d78e9397f146f676cef41b height: height attribute not set width: width attribute not set description: {\displaystyle \pr(x=1)=\pr(u
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f2a23f73879ebc326b524c41e2a14d23318a48c1 height: height attribute not set width: width attribute not set description: {\displaystyle f^{\mathit {inv}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/83b61f89834bd68ce9d89b699dfda812d735550e height: height attribute not set width: width attribute not set description: {\displaystyle {u\leq f(x)}={f^{\mathit {inv}}(u)\leq x}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2e6d5780de5cb8a64b0ebeadd01899ef5bb1e1c4 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)=1-e^{-\lambda x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4fb889e8427ec79417200e4c016790ef0d20c446 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}f(x)=u&\leftrightarrow 1-e^{-\lambda x}=u\\[2pt]&\leftrightarrow e^{-\lambda x}=1-u\\[2pt]&\leftrightarrow -\lambda x=\ln(1-u)\\[2pt]&\leftrightarrow x={\frac {-1}{\lambda }}\ln(1-u)\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f809d85b5b9f0e8db4bffdc50e015f1cc5257c53 height: height attribute not set width: width attribute not set description: {\displaystyle f^{\mathit {inv}}(u)={\frac {-1}{\lambda }}\ln(1-u)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e02942bebf37994c54fa3ebadbd89152b2b4110e height: height attribute not set width: width attribute not set description: {\displaystyle u(0,1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a8614c93305d92695a7ef1638f75c0aab361ef10 height: height attribute not set width: width attribute not set description: {\displaystyle x=f^{\mathit {inv}}(u)={\frac {-1}{\lambda }}\ln(1-u)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a height: height attribute not set width: width attribute not set description: {\displaystyle \lambda } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bcdd1d53d077c41f1f8fc0739dfa264ffeaf4e5f height: height attribute not set width: width attribute not set description: {\textstyle p_{a\leq x\leq b}(t)=\int _{a}^{b}dx\,|\psi (x,t)|^{2}} |
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