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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A question about sampling distribution

Assume there are $n$ independent random variables $X_1,X_2,\ldots,X_n$ and i wonder why the sample variance is $S^2=\frac{\sum\limits_{i=1}^n \ (X_i-X)^2}{n-1}$ where $X$=$\frac{X_1+X_2+\cdots+X_n}{n}$ instead of $S^2=\frac{\sum\limits_{i=1}^{n}\…
johnny
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Marginal distribution functions of two discrete random variables

I am currently taking a probability course based on the book A first course in probability by Sheldon Ross. I have been trying to solve the following problem: $f_{X,Y,Z}(x,y,z) = c$ where $x = 1, 2, ..., y \hspace{5mm} y = 1, 2, ..., z \hspace{5mm}…
Andres
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A decisive test to tell if a function is separable

This is a both physics and math question. I have a Hamiltonian in the form H= q1^2 + q2^2 + q3^2 + q1 x q2 x q3 Therefore the probability distribution will have the form p= exp ^ (-bH) where b is beta/k_b*T Now, I want to know if this…
user178882
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Some issues concerning joint random variables

Let the joint random variable $P[x;y]$ be $P[x;y] = c[2x^2 + y^2], x=-1;0;1, y=1;2;3;4$ $=0$ $elsewhere$ So I had to find the value of $c$ that makes $P[x;y]$ a joint discrete random variable. I think I did that right. I just add up all the…
StephanCasey
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applicability of Poisson distribution

Do all random variables dealing with number of random, independent events in a continuous interval follow a Poisson distribution?
Kishore
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Expectation of function of random variable?

How to calculate the expectation of function of random variable without using probability density function? Note:- only cumulative distribution function is available. For example $E[g(X)]$=? where X is nonnegative r.v. with CDF $F_{X}(x)$.
dikuve
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What is $E[1/X]$ when $X$ is a standard normal random variable?

It's long time ago that I took the calculus class, so I dare to ask. If $X\sim N(0,1)$, what is $\mathbb{E}(1/X)$? $$\mathbb{E}(1/X) = \int_{-\infty}^\infty \frac1x \cdot \frac1{\sqrt{2\pi}} \exp\left(-\frac{x^2}2\right) dx.$$ Can I just claim…
Federico Magallanez
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Probability Distribution, where $E(X^2) = 2E(X)$

May I please get help with this question? What is the answer and how do I get to it? [Within the context of discrete random variables]. Consider a probability distribution where $E(X^2) = 2E(X)$. In this case, the standard deviation is: A. $\sqrt{3}…
user170171
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1 answer

Calculating the variance for m people and n floors

A building has n floors numbered 1, 2, . . . , n, plus a ground floor G. At the ground floor, m people get on the elevator together, and each gets off at a uniformly random one of the n floors (independently of everybody else). What is the variance…
user168915
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Random variable with infinite $(k+1)$th moment

I was asked to give an example of a random variable which has finite $i$'th moments for $i=1,2,\ldots,k$ and has an unbounded $(k+1)$th moment. Obviously, a Student-distributed $t_{k+1}$ random variable will work, but I suppose giving a proof link…
wh1t3cat1k
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P/1 Actuary Exam Question

I was doing problems and came across this one and was wondering why the $P[1\le x\le 2]$ is $F(2) - \lim\limits_{x\rightarrow1^-} F(x)$ rather than $F(2)-F(1)$? Could someone please explain this for me?
Robert Maggio
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Joint density distribution and Variance

I was wondering if there is a way to calculate the joint distribution of two fully correlated variables, both with known distributions, expected value and variance, without knowing the conditional distribution? If this is not possible, is there a…
Captainslow
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Continuous Random Variables: Uniform

Problem: A person drives to work via a road with a single traffic signal. The light cycles, green for 45 seconds, red for 15 seconds – ignore yellow. Assume the person approaches the signal at a random time. Please find: a. the probability of having…
Swamp G
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Poisson distribution given Exponential Distribution

I would need some help on the following problem: We consider two random variables $X$ and $Y$. We suppose that, given X=x, the conditional law of $Y$ is a Poisson distribution of parameter $x$. $X$ follows an exponential distribution of parameter…
XCoder
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Finding a pdf from a CDF with a Discrete Random Variable

I know this question isn't very difficult but I'm not convinced I'm doing it right. For a discrete random variable if you have the CDF, the pdf is defined as $f(x)=F(x)-F(x-)$. I have: $$F(x) =\begin{cases}0,&{x\le…
Vincent
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