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...describe the Pareto distribution. [[Insurance]] companies often use Pareto distributions to model damage. [[Category:Probability distributions]] ...

[[Image:Boxplot vs PDF.svg|thumb|350px|[[Boxplot]] and probability density function of a [[normal distribution]] {{nowrap|''N''(0,&thinsp;''σ' ...obability density function in the interval <math>[a,b]</math> yields the [[probability]] that a given [[random variable]] with the given density is contained in t ...

{{Probability distribution| pdf_image =[[File:Normal distribution pdf.png|325px|Probability density function for the normal distribution]]<br /><small>The green line i ...

...otal variation distance''' measures the difference between two probability distributions. :Let <math>p</math> and <math>q</math> be two probability distributions over the same finite state space <math>\Omega</math>, the '''total variatio ...

[[File:Gumbel-Density.svg|thumb|260px|Gumbel probability distribution function (PDF)]] The '''Gumbel distribution''' is a [[probability distribution]] of extreme values. ...

...e value of [[Pi (mathematics)|π]]. After placing 30,000 random points, the probability that the estimate for π is within 0.07% of the actual value.]] ...get a result. The algorithm terminates with an answer that is correct with probability <math>p<1</math>. ...

'''Probability Theory''' <br> & '''Mathematical Statistics'''</font> |data15 = '''Probability and Random Processes''' (4E) <br> Geoffrey Grimmett and David Stirzaker <br ...

=Coupling of Two Distributions= Coupling is a powerful proof technique in probability theory. It allows us to compare two unrelated variables (or processes) by f ...

We introduce several important distributions induced by independent coin flips (independent probabilistic experiments), ...single (biased) coin flip. Suppose that we flip a (biased) coin where the probability of HEADS is <math>p</math>. Let <math>X</math> be the 0-1 random variable w ...

Let <math>p</math> and <math>q</math> be two probability distributions over <math>\Omega</math>. Give an explicit construction of a coupling <math # with probability <math>p</math>, do nothing; ...

'''Probability Theory''' <br> & '''Mathematical Statistics'''</font> |data15 = '''Probability and Random Processes''' (4E) <br> Geoffrey Grimmett and David Stirzaker <br ...

{{Probability distribution | '''Student's t-distribution''' is a [[probability distribution]] which was developed by [[William Sealy Gosset]] in 1908. ''S ...

...y define this notion, we need a way of measuring the closeness between two distributions. ...otal variation distance''' measures the difference between two probability distributions. ...

|caption = ''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'', Mitzenma # Probability Basics | [http://tcs.nju.edu.cn/slides/random2011/random2.pdf slides] ...

...n to which the ball is assigned is uniformly and independently chosen, the distributions of the loads of bins are identical. Thus <math>\mathbf{E}[X_i]</math> is th ...mum load is <math>O\left(\frac{\log n}{\log\log n}\right)</math> with high probability. ...

...y define this notion, we need a way of measuring the closeness between two distributions. ...otal variation distance''' measures the difference between two probability distributions. ...

...y define this notion, we need a way of measuring the closeness between two distributions. ...otal variation distance''' measures the difference between two probability distributions. ...

* birthday problem: the probability that every bin contains at most one ball (the mapping is 1-1); * coupon collector problem: the probability that every bin contains at least one ball (the mapping is on-to); ...

* birthday problem: the probability that every bin contains at most one ball (the mapping is 1-1); * coupon collector problem: the probability that every bin contains at least one ball (the mapping is on-to); ...

...dom matrix <math>A\in\mathbf{R}^{k\times d}</math> and show that with high probability (<math>1-O(1/n)</math>) it is a good embedding satisfying: and the probability density function is given by <math>p(x)=\frac{1}{\sqrt{2\pi\sigma^2}}\mathr ...