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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Independence in rectangular region

THEOREM: Let random variables $X$ and $Y$ have a continuous joint distribution. Suppose that $\{(x, y) :f(x, y) > 0\}$, (where $f(x,y)$ is a p.f. or p.d.f. or p.f./p.d.f.) is a rectangular region $R$ (possibly unbounded) with sides (if any)…
Silent
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Converses to a commonplace proposition about binomial distributions

I suspect I'll post my own answer to this question shortly, but it may be of interest to see what answers others post. A theorem found in Feller's famous book and elsewhere says that if $X,Y$ are independent random variables and $X+Y$ is normally…
Michael Hardy
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In how many ways can I distribute 6 identical cookies and 6 identical candies to 4 children, if each child must receive exactly 3 items?

I tried to solve this by making a chain of letters, with 'O' representing cookies and 'A' representing candies, as shown below. o o o o o o a a a a a a 1 1 1 2 2 2 3 3 3 4 4 4 This would mean that child one gets 3 cookies, as does child 2, and…
Kevin
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Does the weibull distribution has a sufficient statistic?

When using the following definition of weibull: $f(y) = \beta \alpha y^{\alpha - 1}e^{-\beta y ^ {\alpha}} $ , When $\beta>0 \alpha >0$. I could only find (using the factorization theorem) the following two possible sufficient statistics: $\sum…
Tal Galili
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Speed Networking

For a speed networking session, I would like to have 20 people at 4 tables (5 people per table) move four times during the session to ultimately meet everyone in the session. Is there a formula for seating and moving so that everyone gets to meet…
PSpice
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Compounding a binomial distribution where the number of observation is binomial?

I am looking for a definition of a binomial distribution where the number of observation is itself binomial. That is: $X \sim binom(N, q)$ When $N \sim binom(n, p)$. Is this a known distribution? And how can I find its probability function? Thanks.
Tal Galili
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if X and Y are Gauss distributed, what's the distribution of X^2-Y^2?

X and Y are independent random variables with identical Gaussian distribution; for simplicity, the variance shall be 1. What's the distribution of Z=X^2+Y^2? With a plus sign, it would be the chi-square distribution. The minus sign changes things…
Joachim W
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Books on Probability Theory (for an engineer)

I am an electrical engineering student who deals with probability and stochastic processes for communications systems, but I find that most engineering texts on probability and stochastic processes give very general examples and trivial cases. But…
Phil
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$X$ has a Gamma distribution with parameters $\lambda$ and $\alpha$. Find $E(X^r)$

$X$ has a Gamma distribution with parameters $\lambda$ and $\alpha$. I must find $E(X^r)$ and $r$ is a positive integer. How can I do this? I am guessing I have to use the Gamma function but I don't know how to do this?
savinq
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CDF of a sum of continuous and discrete dependent random variables

Let $\psi_1$ be a Normal random variable with mean $\mu_1$ and standard deviation $\sigma_1$. Let $\xi$ be defined as $$ \xi=c\,\mathbb{1}_{\left\{\psi_2+\psi_1\leq 0\right\}}, $$ where $\mathbb{1}$ is the indicator function, and $\psi_2$ a Normal…
AlmostSureUser
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Finding joint pmfs from marginal pmfs

Let $a, b > 0$. The random variables $X$ and $Y$ are independent and their densities are : $f(x)$ = $1 \gamma(a)*x^{x-1}*e^{-x}, x\geq 0$ $f(y)$ = $1 \gamma(b)*y^{b-1}*e^{-y}, y\geq 0$ Let $U=X+Y$ and $V=X/X+Y$ Find the joint density of U and V and…
fred
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How to quantify uniform distribution?

I have a real-world situation with a machine that lays a layer of wires on a high-pressure hose. The machine has S "slots" (approx 200), and each slot could have one wire or be empty. Typically there are about 100 - 180 wires (W). The objective is…
Tom van Stiphout
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Joint and Marginal distributions of a random sample

Let $X_{1},X_{2},\ldots ,X_{n}$ be a random sample of size $n$ from a population distribution $F$. I want to find the following: 1. the joint P.d.f of $X_{1},X_{2},\ldots ,X_{n}$. 2. the marginal probability distribution of $X_{j}$ for any $j$ in…
Godwin
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Chi squared Distribution WITHIN a tolerance

Learning about the Chi squared distribution - getting familiar with using the tables associated, and trying to understand the curve. Problems such as Are as trivial as looking into the Chi-squared table! Then I was presented with THIS, the final…
PinkElephantsOnParade
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How normal distribution is different from gamma distribution? In theory and practice?

I'm trying to figure out how the normal distribution is different from the gamma distribution in case of theory and practice. Does any one know? Please help.
Sirikarn
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