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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Expectation of S?

There are $n$ marbles and $r$ boxes. One at a time, each marble is selected and randomly (uniformly) placed in one of the $r$ boxes. Let $S$ be the number of empty boxes. Compute $E(S)$ and $Var(S )$. Here is my work: Let $X$ = the box is empty This…
user3904534
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Distribution of minimum of independent dice rolls.

If $\{X_i\}_{1\le i \le n} $ are $n$ independent fair-die rolls, what is the distribution of $\min(X_1, \dots, X_n)$? Let $X := \min(X_1, \dots, X_n), n=$ number of rolls, $P(X = x) = \frac{1}{6}$ Is it correct to say that $X \sim \text{binom}(n, p…
user3904534
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Poisson distribution to normal approximation

Question: Let X have a Poisson distribution with mean 16. Estimate P (X≥28) using the normal approximation. I know that the normal distribution uses the mean and variance. In this case the standard deviation would be √16 which is ~ 4. Do I just use…
Andi
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Distribution of a joint density function.

I have $X$, $Y$ random variables with joint density function $$f_{X,Y}(x,y)=\begin{cases}8xy,& 0
HeMan
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Guessing probability distribution

The question is if probability of bomb hitting a target is 50% and 2 direct hits will destroy the target completely. How many bombs must be dropped to give a 99% chance or better of destroying the target completely? I assume this question can be…
Onix
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how to decide when to generate a particle so that the resulting rate follows a poisson distribution

I am writing a simulator in which I am generating a flow of particle. I want this flow to follow a Poisson process, i.e. $\lambda$ particles are generated per second on average. So how to compute the time of the next particle generation? i.e. how to…
brice rebsamen
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Why is random variate T of student's t-distribution defined the way it is?

I recently learned about t-distribution and I didn't find it very obvious as to why $T$ is defined as $T=\frac{W}{\sqrt{V/r}}$, where W is a standard normal variate and $V$ follows a chi-sqaure distribution. What lead to this definition of T ?
Zanylytical Scientist
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probability function $f(x)= \frac{c}{3^x}$, x=1,2,3... determine the constant c and find the distribution function.

This question is from schaums probability and statistics: probability function f(x)= c/3^x, {x=1,2,3...} determine the constant c and find the distribution function. The answer in the back of the book is c=2 but I get 2/3 since: \sigma$$\sigma$$…
billnyeguy
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Poisson Distribution Problem.

I have this problem that I think I've kind of solved but just wanted to make sure if it's correct. The problem goes: The homework submissions to the university computer center start at midnight (00:00). The number of homework submissions between…
Cheul Hee Jason Yoo
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Geometric distribution after $n$ trials

Find the probability of $x$ happening for the first time after $n = 1000$ trials with $p = 0.001$ So after $n$, I'm assuming that this means at most $n$? I know the generic way of solving at most which would be: $$p(0) + p(1) + \cdots + p(n)$$ but…
user3538161
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Term for $P(Z > z)$?

I know that $P(Z \leq z)$ is considered the CDF of the random variable $Z$ but is there a term for $P(Z > z)$? For example, if $Z \sim \mathrm{Exp}[\lambda]$, what is $P(Z>z)$?
David South
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Exponential distribution of x between 2 values

Given: On the average, 10 calls were received in an hour I can solve the first two probabilities whereas: The probability that a call will be received after 8 minutes is $$e^{\mu t} = e^{-10\frac{8}{60}} $$ is 0.2636 and, The probability that a call…
Florencio
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Product of Lognormal PDF and Normal CDF

For one of the engineering applications, we are required to calculate the integral of the product of a lognormal PDF and normal CDF. Essentially, the probablity of event occurance has a lognormal distribution, but once the event occurs, the…
PJn
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Calculating PDF of consequent events

My question is how to calculate the probability density function (pdf) of consequent, but otherwise independent events, defined as follows (in case of 3 events): $A$ is an independent event with pdf $f(x)=\lambda_1 e^{-\lambda_1x} $. $P(B|A')=0$,…
Anna401
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On Wishart Distributions

Notation: Let $S$ is a complex square matrix. ${S}^H$ denotes conjugate transpose matrix, while $[S]_{k,k}$ denotes the k-th diagonal element, and $S^{-1}$ denotes the inverse matrix. Let $S=GG^{H}$ be a positive definite matrix where all elements…
pej
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