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.

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Find the probability density function of $Y=|Ax+n|^2$

I know that the pdf of $Ax+n$ is a Gaussian one and I want to calculate the pdf of $Y=|Ax+n|^2$. Is this possible?
Marios
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What is the distribution of $Y = X^2$ given $X$ is Student's $t$ with $k$ df?

Given a random variable $X$ being a Student's $t$ with $k$ degrees of freedom, find the distribution of $Y = X^2$. $$f_X(x;k) = \frac{\Gamma\left(\frac{k+1}{2}\right)}{\sqrt{k\pi} \ \Gamma…
Gabriel Vivaldini
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Probability of getting a matching pair of socks

A drawer contains 3 black socks, 4 red socks and 6 white socks. What is the probability that there is a matching pair of socks if three socks are taken from the drawer at random?
Mary
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Probability mass function

An insurance agent has two clients each of whom has a life insurance policy that pays 100000 dollars upon death. Their probabilities of dying this year are .05 and .1. Let X denote the total amount of money that will be paid this year to the clients…
bob
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Generate coefficients of fading channel (lognormal + Rayleigh)

This question concerns fading channels in wireless communication, but its essence is still statistics and distributions, so I pose it here. I want to generate (sample) complex-valued coefficients that model the wireless channel by taking into…
index
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What kind of distribution is this and how can it be approximated to a continuous one?

$p(x) = e^{-x\beta}(1-e^{-\beta})$ Where $x$ is integer takinng values as $x = \{0, 1, 2, ...\}$ and $\beta > 0 $ is a real constant. Is this a Poissonian distribution? and how could I approximate it in order to sample continuous random variables. I…
Magil
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Show 1/X is F(n,m) if X is F(m,n)

How to show this? F is the Fisher–Snedecor distribution, B is the beta function. This is what i have done $$Y=\frac{1}{X}$$ $$f_{Y}(y)=f_{X}(1/y)\times…
Sofia Fredriksson
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A priori probability distribution of n non-negative reals with constant sum S

Suppose you have $n$ non-negative real numbers $x_{1}, \ldots , x_{n}$ such that their sum $\sum^{n}_{i=1} x_{i} = S$. What is the a priori probability distribution over the possible values of a single $x_{i}$?
Timothy Ranallo-Benavidez
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How to derive the cumulative density function of $X>0$ from the characteristic function of $Y=X^2$?

Which is the relation (can the 1st be derived knowing the 2nd) between the cumulative density function of positive rv $X>0$$CDF_X(x)=Prob(C<=x)$ and the characteristic function of $Y=X^2$: $CF_{Y}(z)=E[e^{izY}]$? CONSTRAINT: The probability density…
Gabriele Pompa
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Discrete probability distribution: is the game fair?

A and B play a game by rolling 2 dice. A gets 5 points if he rolls a double (both dice the same), otherwise he loses 1 point. Is the game fair? What is the expectation gain or loss for A? Is probability distribution table necessary? I tried…
frizz
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Bivariate normal concave downwards

The Hessian matrix of the bivariate standard normal distribution (where both standard normal distributions are independent) is positive definite. Yet, it concaves downwards. If the Hessian is positive definite, shouldn't that mean that the function…
darkgbm
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Expected Frequency distribution of numbers for a pick 5 from 35 lottery.

There is a Pick 5 from 35 lottery called Mass Cash. It has had 4,073 drawings over its history so far. What would be the expected frequency of a given number being drawn, assuming each number has an equal chance of being drawn over the life of…
Kosh
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Finding the Integral´s interval for a Probability Function

The probability density function of a given random variable is given by the graph below. How can I set up the integral in order to find P(X>0, P(X>3/4). I tried to set up the integral and this is my attempt. For the P(X>0, P(X>3/4), I have set…
Vinicius L. Beserra
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Average distance between remaining un-hit targets as targets are progressively hit

Consider targets arranged in a regularly spaced array across a near-infinite X-Y plane (area of plane is large relative to area of a target). Each target is initially a unit distance from adjacent targets. Targets exist initially as open. Targets…
user73522
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Generating samples from a Beta(2,2) distribution

I'm looking for a convenient way to generate $\text{Beta}(2,2)$ random variables, using independent $\text{Uniform}(0,1)$ random variables and elementary functions. I'd prefer to avoid rejection or iterative methods. The PDF is $6 x (1-x)$. The CDF…
Benjamin Roycraft
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