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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What is the pdf of $X/Y$, where $X$ has a symmetrical uniform distribution, and $Y$ is normal with mean zero?

If X has a uniform distribution, between some -L and L, and Y has a normal distribution, with zero mean and variance=Sigma^2. The distribution of Q=Y/X is called the "Slash distribution". https://en.wikipedia.org/wiki/Slash_distribution How to…
user1611107
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How to determine Y(n)

A random variable $x$ from the set $\{1, 2, ... ,n\}. $ Let $x$ has distribution function $f(k) = Y(n) · g^k$ where $g$ is a fixed number within $0$ and $1$. Find $Y(n)$ which is a constant term in terms of n. I do not know how to determine…
Www
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Is P(A≤−B)= 1− P(A≤B) an correct equation?

Is P(A≤−B)= 1− P(A≤B) an correct equation? If yes, kindly provide the derivation of the same. As I get it, P(A≤−B)= 1− P(A>−B) i.e. 1−P(−A
Pankaj Kumar Swain
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Calculating $P(2\leq X\leq 4)$ for an exponentially random variable

While calculating P(2≤X≤4), for an exponential random distribution, the solution says, $P(2\leq X\leq 4) = F(4)-F(2)$, where F denotes the CDF. My version is, P(2≤X≤4) = P(22) and P(X≤4), i.e. 1-P(X≤2) and P(X≤4) {1-F(2)} * F(4), presuming they…
Pankaj Kumar Swain
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Joint distribution of two Gaussian random variables

We have two independent Gaussian random variables with zero mean and variance $\sigma^2$, i.e., $\theta_V \sim \mathcal{N}(0,\sigma^2)$ and $\theta_H \sim \mathcal{N}(0,\sigma^2)$. Let $X=\theta_V^2+\theta_H^2$ and $Y=2\theta_V^2+2\theta_H^2+\alpha…
Hui Zhao
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Poisson distribution: trucks and cars

This is some probability problem that I conjured up. Can anyone check whether this problem makes sense and has a solution? Assume that the traffic on Spooner street follows a Poisson process with a rate 2/3's of a vehicle per hour. 10% of the…
Federico Magallanez
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A and B play a game with colored balls. A starts with 6 balls: 2 orange, 2 yellow and 2 green. B starts with 4 balls: 2 pinks ...

CONTD. $A$ and $B$ play a game with colored balls. $A$ starts with $6$ balls: $2$ orange, $2$ yellow and $2$ green. $B$ starts with $4$ balls: $2$ pinks and $2$ gray. Player "$A$" plays first, and both alternate turns. On each turn, the player…
CarolineSerge
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Normalize a probability density function

Suppose you have two independent variables with equal density function $p(x|\omega_i)\propto e^{(-|x-a_i|/b_i)}$ for $i=1,2$ and $0
Lucy_in_the_sky_with_diamonds
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How to create two independent exponential distributions from two arbitrary exponential distributions.

In the normal case, we know that if an $n-$dimensional random variable $X$ has a multivariate normal distribution with mean vector $\mu\in \mathbb{R}^n$ and covariance matrix $C\in \mathbb{R}^n \times \mathbb{R}^n$, i.e., $X\sim \mathcal{N}(\mu,C)$,…
admath
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Show that $Y=\lfloor X\rfloor+1$ where $X$ is exponential is a geometric distribution?

Given the exponential distribution, $X$ with rate $\lambda$ define $Y=\lfloor X\rfloor+1$. Show that $Y$ is geometric with $p=1-e^{-\lambda}$. Work $$f(y) = P(Y=y)$$ $$=P(\lfloor X \rfloor + 1=y) $$ $$= P(\lfloor X \rfloor=y-1) $$ $$=…
Jac Frall
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Computing partial moments of the lomax distribution

I have a variable that is distributed according to a lomax distribution (https://en.wikipedia.org/wiki/Lomax_distribution) with CDF and PDF given by $F(x) = 1-\left(1+x\right)^{-\alpha}$ $f(x) = \alpha(1+x)^{-\alpha-1}$ I know that moments are given…
j steinberg
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What is this linear-fractional distribution formula missing?

See Definition 1 in this paper: http://arxiv.org/pdf/1111.4689v3.pdf The left-hand-side of the second formula appears to suggest some kind of recursion, but the right hand side is not a recursive expression. The right hand side depends on $i$ but…
wircho
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Name of the distribution $p^x(1-p)^{1-x}$?

We are given a random variable $X$ with PDF: \begin{align*} f(x ; p) &= p^x(1-p)^{1-x} \ , \\ \end{align*} where $0 \leq p \leq 1$ is the parameter and the support is $x \in \{0,1\}$. Anyone knows what the name of this distribution is? And if so,…
KareemJ
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Cumulative Distribution Fit

I am looking for a monotonically decreasing function to fit a cumulative distribution. The distribution is the number of values of a random variable X, that are greater than Y as a function of Y. In total, there are a few hundred values of X so the…
Jim Adams
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How to find the marginal density here in the question given?

Let $Y$ have a uniform distribution on the interval $(0, 1)$, and let the conditional density of $X$ given $Y = y$ be uniform on the interval from $0$ to $\sqrt{y}$. What is the marginal density of $X$ for $0 < x < 1$?
Gaurav Kumar
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