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
4
votes
2 answers

Find the probability for having real roots with the polynomial $x^2+ax+b$

Choose two real numbers $a$ and $b$ satisfying $1
Diakolo Belya
  • 59
  • 4
4
votes
2 answers

Expectation and variance of the geometric distribution

How can one use memorylessness and the law of total expectation and the law of total variance to find the expectation and variance of the geometric distribution? I will post my own answer, but as always, that shouldn't stop anyone else from posting…
Michael Hardy
  • 1
4
votes
1 answer

Marginal distribution is negative binomial under Poisson distribution with Gamma prior

Suppose we have random variable $Y$ has the Poisson distribution with parameter $\theta$, and $\theta$ has a Gamma prior distribution, i.e. $$\begin{aligned} & \text{Data: }\hspace{1cm} y\mid\theta \sim \operatorname{Poisson}(\theta)\\ &…
Matata
  • 2,088
4
votes
0 answers

Joint pdf, conditional density and correlation between max and min of two independant exponetially distributed variables

I am trying to solve this problem where instead of uniform distribution, x and y are distributed EXP(1/b): Suppose X and Y are two independent random variables, both uniformly distributed on (0,1). Let T1 = min(X; Y ) and T2 = max(X; Y ). 1) What is…
mpjunior
  • 41
4
votes
1 answer

Asking for help with E(X(E(Y|X))

This is problem 6.9 in Ross. I have the joint pdf $$f(x,y) = 6/7(x^2+xy/2), 0
asahi
  • 209
4
votes
0 answers

Help identify this (heavy-tailed?) distribution

I have a data set with approximately $10\ 000$ samples of a random variable which takes values in the interval $[0,1]$. I am interested in finding out if this variables follows any well-known distribution, even approximately. I started by using…
David M.
  • 2,623
4
votes
1 answer

Sum of exponential random variables with different parameters - followup

It has been well known that if $X_1$,...,$X_n$ are independent exponential random variables with common parameter $\mu$, then we have a gamma distribution $\sum_{i = 1}^{n}X_i \sim \Gamma(n,\mu)$ with two parameters $(n, \mu)$. My question is do we…
Liäm
  • 111
4
votes
0 answers

Hellinger Distance between Laplace Distributions

I'm looking for a closed form for the Hellinger distance between two (generalized) Laplace distribution with the same covariance (but different means). Any suggestions? Thanks in advance, Federico
Federico
  • 41
4
votes
2 answers

Two Coins are Flipped n Times

So two people are flipping a fair coin $n$ times each. What's the probability that they both flip the same number of heads? My current approach was to use a binomial, and sum up the cases when X (no of heads) = 0,1,...,n But was wondering if there…
An Invisible Carrot
  • 420
4
votes
2 answers

What is the density of the sum $Z = X+Y$?

Find the density of the sum $Z = X+Y$ when $X$ and $Y$ are independent, standard uniform random variables. $$f_X(x) = 1\quad\mathrm{if}\quad 0\le x \le 1$$ $$f_Y(y) = 1\quad\mathrm{if}\quad 0\le y\le 1$$ $$\begin{align} f_Z(z) & =…
woaini
  • 335
  • 1
  • 5
  • 18
4
votes
2 answers

Monotone likelihood ratio without densities

I would like to find a generalization of the monotone likelihood ratio ordering that does not require that the probability distributions admit a density and have the same support, which would allow me to deal with degenerate probability…
Oliv
  • 447
4
votes
2 answers

Conditional distribution of continuous random variable $X$ given $|X|$?

If a continuous random variable $X$ has a symmetric distribution around $0$, what is the conditional distribution of $X$ given $|X|$?
ie86
  • 489
4
votes
2 answers

What does "over the unit square" mean?

So i was told that a joint distribution of two volumes $X$ and $Y$ (both ranging from 0 to 1) is $f(x)=c(x+y^2)$ over the unit square, 0 otherwise. My question might be trivial, but I've never seen this expression before, what does "over the unit…
BKS
  • 167
4
votes
2 answers

Suppose you have 'n' identically distributed, independent random variables, what is the pdf of the max(),min() of those variables?

Let $X_1, X_2, ...,X_n$ denote independent and identically distributed (iid) random variables (r.v) each with pdf $f_x(x)$. The (homework) problem asks me to consider the function: Y = min{$X_1,X_2,...,X_n$} And the goal is to find the PDF of Y.…
Minh Tran
  • 321
  • 1
  • 6
  • 16
4
votes
1 answer

Weighted hypergeometric distribution

The probablility of $M$ successes out of $N$ draws without replacement from a population of $S$ success and $F$ failure states, assuming that each remaining state is equally likely, is given by $\dfrac{\binom{S}{M}…
Jesper Larsson
  • 143
  • 6
1 2 3
…
99 100