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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Two stochastic variables

Say $Y$ is the nummer of accidents by a car, Poisson distributed ($\lambda$). People hit by the car have a probability $p=\frac{1}{2}$ to survive. Let $Z$ be the nummer of people killed by a car accident. Now I want to determine $P(Z=k)$ for…
iJup
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If the joint distribution is uniform, then the random variables are independent?

This is a problem that I am stuck at. If $X_1$ and $X_2$ are independent, it would be easier. But, the problem asks me the converse. For (i), I suspect that $X_1$ and $X_2$ are independent. But I find no way of showing this. For (ii), I even have…
Keith
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The sum of infinitely many independent Poisson random variables.

I'll post my own answer to this unless someone beats me to it and maybe even after ten others are posted in the first ten minutes, but of course there may be many ways to prove the result, so post your own if it's different and worth seeing. Suppose…
Michael Hardy
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Joint Density of N Dependent Uniformly Distributed Random Variables

Could someone show me the formula with proof for the Joint Density and CDF for N uniformly distributed variables that are not necessarily independent? Again, if certain forms of dependence are assumed, please point that out in the answer. Thanks in…
texmex
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Combination of two bivariate Gaussian covariance matrices

I have measurements of 2 position vectors ($\mathbf p_1$ and $\mathbf p_2$): Each with their own mean position vectors $(\overline x_1, \overline y_1, \overline z_1)^T$ and $(\overline x_2,\overline y_2,\overline z_2)^T$ respectively, Each with…
ZBC
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Average Waiting Time for mixed distribution function

Mixed Distribution Function $$ F(t) = \begin{cases} \hfill 0 \hfill & t < 0 \\ \hfill p+(1-p)(1-e^{-yt}) & t \geq 0 \end{cases} $$ How can i find the average waiting time of an arrival and average waiting time for an arrival given that a…
Jake
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Expected no of balls to select before a certain type of ball comes

There are w white balls and r red balls in a box, to find the expected no of balls to pick before we get a red ball? $$\qquad$$ What I have tried is, Let $ X_k $ denote that k no of white balls have been taken out before we get a red ball, clearly…
Cloverr
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Distribution of sum of $m$ independent random variables

Let $A_m$ be the sum of $m$ identically distributed random variables that are independent and that have an exponential distribution with parameter $\mu$. How do I prove that $A_m$ has a gamma distribution with parameters $m$ and $\mu$? And how do I…
Stan_Allen
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joint distribution marginalization proof, is this right?

prove: $$p(x\mid z) = \sum_y p(x\mid y,z)p(y\mid z)$$ I understand a bit about marginalization. I think my prove should look like this: $$ p(x\mid z) = \sum_y p(x,y\mid z) = \sum_y p(x\mid y,z)p(y) $$ My first portion, where I add the sum of y in,…
still learning
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Distribution and density function of $Y=\frac{3X}{1-X}$

Let X be a random variable that is uniformly distributed on $[0,1]$. What are the distribution and probability density functions of $Y$ with $Y=\frac{3X}{1-X}$? I know that the density is the derivative of the distribution function, so if someone…
JimmyP
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Expected ratio of successes of Bernoulli provided total number of trials is N

My question seems similar but not exactly explained by negative binomial If I stop experiment when either k successes is reached or after N experiment What is the expected ratio success/required number of experiments Seems like limited case of…
sasha
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Definition and statistics of the Negative-Hypergeometric distribution

The Encyclopedia of Mathematics defines the Negative Hypergeometric distribution (NHG) in the following way: There are $N$ elements, of which $M$ are marked and the rest are unmarked. Elements are drawn at random without replacement, until the…
Erel Segal-Halevi
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Is there a probability distribution with the following properties?

I'm looking for a univariate probability distribution defined for $x \in (-\infty, \infty)$ with the following properties: The PDF is symmetric around the origin ($p(x)=p(-x)$). The derivative of the PDF at $x=0$ (with the limit taken from above)…
Johannes
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Probabiliy Distribution Proof

Please help and provide suggestions. (i) A discrete random variable X has the distribution $P(X = i) = 2a^i $ for i ∈ N+ (where N+ := {1,2,...}). What is the value of a? $P(X = 1) = 2a^1 ;P(X = 2) = 2a^2 ;P(X = 1) = 2a^3 ;P(X = 1) = 2a^4;......…
user117498
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$X,Y$ are independent exponentially distributed then what is the distribution of $X/(1+Y)$

If $X$ and $Y$ are independent and exponentially distributed, which is the pdf of $Z$? Where $Z$ is given by \begin{equation} Z = \frac{X}{1+Y} \end{equation} I read similar posts on this forum but those are all different cases. $X,Y$ are…
smtux
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