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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Finding PDF of random variables

Let $X$ and $Y$ be random variable with joint pdf: $$f(x,y)= \begin{cases} \frac{1}{4} e^{-\frac{1}{2}(x+y)} & x \geq 0, y \geq 0 \\ 0 & \text{ otherwise} \end{cases} $$ $U= \frac{1}{2}(X-Y)$, $V=Y$. I know that $f(u,v)=…
fred
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Probability generating function of geometric distribution

For a geometric distribution with $p_{x}(x)=p(1-p)^x, x=0,1,2,3,...$ I have been asked to find the probability generating function. I know that the way to find this is by finding $E(s^x)$ (the expectation) but I've plugged in the probability mass…
George
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which one of the following probability mass function can define a probability distribution?

a) $f(x)=(5-x^2)/6$ for $x=0,1,2,3$ b) $f(x)=x/15$ for $x=1,2,3,4,5$ c) $f(x)=1/2^x$ for $x=0,1,2,3,4$ d) $f(x)=1/4$ for $x=2,3,4,5,6$ Can you please suggest me how to solve these questions ?
PallaviBatra
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p.d.f of function of random variable

Suppose $X$ is a continuous random variable with p.d.f: $$ f_X(x) = \begin{cases}1 & x \in [0, \frac{1}{2}) \\ 1 & x \in [1, \frac{3}{2}) \\ 0 & \text{otherwise} \end{cases} $$ What is the p.d.f of $Y = {(X - 1)}^2$? Let's plot $g(X) = {(X - 1)}^2$…
David Robert Jones
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Find the density function of the wait time of a local forecast

A weather channel has the local forecast on the hour and at 10, 25, 30, 45, and 55 minutes past. Suppose that you wake up in the middle of the night and turn on the TV and let X be the time you have to wait to see the local forecast, measured in…
EggHead
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Help solving: Problem on Normal Distribution of Data

A statistical analysis of 1,000 long-distance phone calls made from a mobile phone indicates that the length of these calls is normally distributed. It is known that half of these phone calls are less than or equal to 240 seconds duration and the…
OneQuestionOnly
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binomial distribution with replacing the opposite color of the items.

I'm not sure which discrete probability distribution to use for this kind of problem. We are given two sets of balls n blue and m red. This is very similar to a binomial distribution except that every time that when drawing a ball at random, when a…
pyCthon
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Probability Distribution Of Sum of a Bernoulli and a Geometric Random Variable

Let X~Bernoulli$(\theta)$ and Y~Geometric$(\theta)$ where X and Y are independent. Let Z = X + Y. What is the probability function of Z? My thoughts are: Let Y be the number of failures until the first success. $p_Z(0) = p_X(0)p_Y(0) = (1 -…
EggHead
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CDF of $X$ from joint CDF of $(X,Y)$

This question is from DeGroot's "Probability and Statistics"(Second Edition). Suppose that $X$ and $Y$ are random variables that can only take values in the interval $0\leq X\leq2$ and $0\leq Y\leq2$. Suppose also that the joint CDF of $X$ and $Y$…
Silent
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How to calculate (discrete) Pareto distribution. e.g., Probability that someone is in (an arbitrary jellybean giving) secondary sub set.

Assuming two equal sized populations (A & B), 20% of group A has been given one or more jelly beans (arbitrary distinction) by one or more people group B. The subset in group B (B1) who gives away jelly beans follow, a Pareto distribution. So some…
DarcyThomas
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Probability Distribution on a 1D space with curvature

Can one consider that a general probability distribution for some random variable X over a Euclidean space is actually the probability distribution of a uniform random variable over a curved 1D-space ? (I was thinking about a map of the type…
AlexPof
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Unbiased estimator for geomtric distribution

The number of persons coming through a blood bank until the first person with type A blood is found is a random variable Y with a geometric distribution , i.e.: p(y) = (1-p)y-1 (p) 0 ≤p ≤ 1 If p denotes the probability that any one randomly…
Chris
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If X is Erlang$(k_1,\lambda)$ and Y is Erlang$(k_2,\lambda)$, then is X+Y Erlang$(k_1+k_2,\lambda)$?

If X is Erlang$(k_1,\lambda)$ and Y is Erlang$(k_2,\lambda)$, then is X+Y Erlang$(k_1+k_2,\lambda)$? Do X and Y need to be independent?
Jim
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what is the probability that the first account containing substantial errors is the third one to be audited

a certified accountant has found that 9 of 10 company audits is the third one to be audited. the accountant audits a series of company accounts what is the probability that the first account containing substantial errors is the third one to be…
jay
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Why $P(A|X=x) = x$ ? X that has a continuous distribution with $E(X) = 0.5$ and $σ(X) = 0.01$, A is define tails was obtained in a 1 toss of the coin

A coin factory produces coins with a probability of getting “tails” X that has a continuous distribution with expectation $0.5$ and standard deviation $0.01$. A person chooses a random coin that is produced in the factory. Suppose that event A is…
DanielMa
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