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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PDF for the square of a multivariate Gaussian

Suppose I have a vector of random variables $\mathbf{X}$ whose pdf is given by a multivariate Gaussian $\mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$. What is the pdf for the joint distribution of the element-wise square of the random…
user2452976
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probability (spread a rumor)

In a room with $n+1$ people, a person tells a rumor to another person, who in turn repeats it to a third person, and the process continues. at each step the receipt of the rumor is randomly chosen out of the n other people in the room. a). Find the…
Deepsea234
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Linearly distorting the distribution of random numbers?

I don't know any math notation, so I'll just write in plain english. Though it isn't too important, I'm working in Javascript. What I want to know is basically this question on stack overflow, though I think it's more appropriate for here, and it…
wwaawaw
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Suppose that $f(x_1,y_1)f(x_2,y_2) \le f(x_1,y_2)f(x_2,y_1)$ holds for $x_1 \le a \le x_2$ and $y_1 \le b \le y_2$ .

Let $(X,Y)$ have the joint density function $f$ and joint distribution function $F$.Suppose that $f(x_1,y_1)f(x_2,y_2) \le f(x_1,y_2)f(x_2,y_1)$ holds for $x_1 \le a \le x_2$ and $y_1 \le b \le y_2$ .Show that $F(a,b) \le F_{x}(a)F_{y}(b) $ where…
user321656
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Distribution of $r.(\ln(X)-X)$ when $X$ is beta distributed.

I need some help and this is certainly not a home work question, as it appears in my research. If $X$ is a beta distributed random variable, is there a known distribution for \begin{equation} \begin{split} Y & =…
user2167741
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How can I calculate the expected profit in this exercise?

A compressor manufacturer offers a five year warranty on repair or replacement of a compressor for its first fault. It is known that the time a compressor operates before failure is a continuous random variable $T$ with density function …
Aarón David Arroyo Torres
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Probability distribution function of $x^n+y^n$ when $x,y$ are normally distributed?

Say I have two random variables, $x,y$ that are independent and normally distributed, $\mathcal{N}(0,1)$. What is the probability distribution function of $r$ and $r^2$ where $r=\sqrt{x^n+y^n}$ and $n$ is a positive even integer? It is known that…
xadu
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bag of 20 marbles, at least 19 are white, 20th is red with prob. P. What is likelihood of finding red on successive draws?

I have bag of 20 marbles, at least 19 of which are white, 20th marble may be red with prob. P. I plan to draw marbles one at a time till I find the red marble or all marbles are used up. At start, I believe I can say that probability that I will…
George
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Is there a formal name for this "weighted probability distribution"?

This type of simple encoding of probability distributions is used commonly in algorithms, among other things, but I don't know what to call it: If you have a set of outcomes: $X = \{x_1, x_2, x_3, ... x_n\}$ And associate a non-negative value (in my…
Tim Atkinson
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What is the pdf of $Z=XY^3$ given the joint pdf of X and Y?

Let X and Y be continuous, with joint pdf: \[ f_{X,Y} = \begin{cases} 2, & \text{if 0 < x < 1, 0 < y < x} \\ 0, & \text{otherwise} \\ \end{cases} \] Let $Z = XY^3$. What is the pdf of Z? I was thinking that maybe I could let W be another function of…
woaini
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I need any equation to solve the required operation

I am trying to create a calculator. A=low B=low C=low A=low B=high C=high A=high B=low C=low A=high B=high C=very-high Update I am trying to create a calculator. where A is the…
Jithin
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Ornstein-Uhlenbeck process

For a Brownian motion $(X_t)$ where $0≤t≤1$ define $(Y_t)=e^{-t}X_{e^{2t}}$ for $t\in R$ What is the distribution of $Y_t$ for a given $t \in R$? It should be distributed like an Ornstein-Uhlenbeck process but I have no clue why and how to show it.…
Jynne94.
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If A ~ Poisson(a), then what is joint probability mass function of male and female fish?

Suppose that the number of fish in a big sea $A$ adheres to a Poisson distribution. What is joint probability mass function of having $x$ male and $y$ female fish? I thought that I could just divide A by $\frac{1}{2}$ and add the two together... but…
John Hoffman
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Where did $\lambda$ come from?

Each second, an ounce of a radioactive substance poissonium emits 5 alpha particles on average. Approximate the probability that exactly 4 alpha particles are emitted by an ounce of poissonium over the next second. I am told that I can use a poisson…
John Hoffman
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How many numbers will I get right?

I play a guessing game. In this game, there are 100 equally-sized, folded-up cards randomly dispersed in a bag. The cards are labeled 1 through 100. I draw out the cards one by one and try to guess the number on the card every time I draw. On every…
Minden Petrofsky
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