Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

28080 questions
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Bounded simulations between Bernoulli distributions

Let $B(p)$ be the Bernoulli distribution associated to the probability $p$. Let $(→)$ be the relation such that $(p→q)$ iff you can generate $B(q)$ from $B(p)$ with a bounded number of draws. (This implies that rejection sampling is not relevant…
jmad
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Flat product distribution

When $X,Y$ are iid random variables, uniformly distributed on $[0,1]$, then $Z=X*Y$ has the density $-\log(z)$, as it is shown here: product distribution of two uniform distribution, what about 3 or more The question is: For which density of $X,Y$…
Daniel Siebert
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If $X,Y$ standard normal, find conditional distribution of $X+Y$ given $X>0$ and $Y>0$

The (old qualifying exam) question is this: if $X,Y$ are independent standard normals, what is the distribution of $Z=X+Y$ given that $X>0,Y>0$? We must find $P(Z\le z, X>0,Y>0)$ (and then divide this by $P(X>0,Y>0)=\frac14$), which means…
Mike Earnest
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Can you explain Moment generation Function (MGF)?

I am not from a Math field, but use statistics. I am having a tough time understanding the concept of a moment generating function. I use PDF's mostly to characterize my data. What are the possible advantages of working with MGFs?
tristarbluehead
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Range of i.i.d. normal random variables

Let $X_1, \dotsc, X_n$ be i.i.d. standard normal random variables. Define the range $R \in \mathbb{R}_{\geq 0}$ as $R = \max \{X_1, \dotsc, X_n\} - \min \{X_1, \dotsc, X_n \}$. I am looking for a simple expression that is a good approximation of…
WimC
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Intuition Behind Power Law Distribution

I know that the pdf of a power law distribution is $$ p(x) = \frac{\alpha-1}{x_{\text{min}}} \left(\frac{x}{x_{\text{min}}} \right)^{-\alpha}$$ But what does it intuitively mean if, for example, stock prices follow a power law distribution? Does…
Thomas James
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Negative Binomial Distribution

Why is the negative binomial distribution defined as $$P(X=x|r,p)= \binom{x-1}{r-1}p^{r}(1-p)^{x-r}$$ Basically this is the probability that $x$ Bernoulli trials are needed for $r$ successes. So we need $r-1$ successes in the first $x-1$ trials.…
Toby
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Does a continuous probability density function (pdf) have zero values on +infinity and -infinity?

Assume a pdf $f(x)$ is continuous along $-\infty$ to $+\infty$. Does this assumption guarantee that $f(+\infty)=f(-\infty)=0$? How to prove? Thanks in advance.
MIMIGA
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The expectation of the half-normal distribution

For the density function below, I need to find $E(X)$ and $E(X^2)$. For $E(X)$, I did the following steps and got the answer of $-2/\sqrt{2\pi}$. However, this is incorrect as the correct answer is $\sqrt{\frac{2}{\pi}}$. I am unsure what I did…
icobes
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Singular Distribution

In reading section 2.2, page 14 of this book, I came across the term "singular distribution". Apparently, a multivariate Gaussian distribution is singular if and only if its covariance matrix is singular. One way (the only way?) the covariance…
Gus
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calculate the Probability density function of the absolute difference of two random variable

If $X$ and $Y$ are two independent random variables with probability density functions $f$ and $g$, respectively, then the probability density of the difference $Y − X$ is given by the cross-correlation . In contrast, the convolution f * g gives the…
skyde
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Is this possible to have these couple of dice?

This problem was proposed to me at a job interview. Suppose you want two dice, both with 6 faces. The first dice has faces with values in $\{1,2,3,4\}$, the other can take values in all $\mathbb N$. Well now we consider the classical random variable…
oxedex
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How do I compute this probability distribution?

Choose a random number uniformly over the unit interval $x_1 \in [0,1]$. Now chose a second number that is dependent on the first, such that it is chosen uniformly over the interval $x_2 \in [0, x_1]$. What is the probability distribution $x_2$? Is…
Hooked
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exponential distribution - get some meaning

I read that a continuous random variable having an exponential distribution can be used to model inter-event arrival times in a Poisson process. Examples included the times when asteroids hit the earth, when earthquakes happen, when calls are…
havingacokewithice
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A Bernoulli trials problem

Two parents decide to have children until they have 3 children of the same gender one after another (3 in a row). If p(boy)=p(girl)=1/2, how many children are they expected to have? I have tried to draw a tree diagram to analyse the problem, but i…
Y-dog
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