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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probability Y> max of independent random variables with same distribution, different means

I am extremely enthused at finding this website. Thanks to Dilip Sarwate for some comments. I still don't have a final solution, however. Below is edited to better focus the problem. Here is my problem. The situation is N random variables X(i), and…
Randy V
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What is this disrtibution being called? $g_{r}(x) = cx^{-r}\chi _{(1,\infty)}(x)$

I have a pdf $g_{r}: \mathbb{R}\rightarrow \mathbb{R}, r>1,c \in \mathbb{R}$ with $g_{r}(x) = cx^{-r}\chi _{(1,\infty)}(x)$. I am currently creating a list of all distributions we have covered in my stochastics lectures and homework and I wondered…
JimTrouserHead
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Distribution of negative of a random variable

A random variables $X \in N(0,1)$, i.e. $f_X(x)=\frac{1}{\sqrt{(2\pi)}}e^{-\frac{x^2}{2}}$. If I define a new random variable $Y=-X$. What is the density function of the $Y$? If I then want to find cumulative distribution function of $Y$ how would I…
cjkilimanjaro
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Does Xn converge to Po(λ) if Yn does?

Suppose that Yn is known to converge in distribution to Po(λ) as n-> ∞. We also know that E[Xn] = E[Yn] for all values of n. Can we then assert that Xn converges in distribution to Po(λ)?
Todd Davidson
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Proving a statistic is ancillary [link to an old question]

It seemed pointless to write in the comments due to the question being old. There is one question given here with an accepted answer that I can't understand. It is implied there that from two random variables having the same distribution it follows…
Nikita Dezhic
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Joint distribution table

A fair coin is tossed four times. Let X and Y be the numbers of tails obtained in the first two tosses and the last three tosses, respectively. $(a)$ State the distributions of X and Y . $(b)$ Describe the joint distribution of X and Y by a…
user720013
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How to prove this conditional distribution is uniform?

Let $X_1$ and $X_2$ be two independent and identically distributed random variables having geometric distribution. The pmf is of the form $q^xp$, $x=0,1,2,...$ to infinity. I have to show $X_1=x_1|X_1+X_2=t$ has uniform distribution. I took…
AP _
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Can someone explain the derivation to me?

This is from some class notes of a friend. In the line marked as (??), I can’t understand the inclusion of -2. When x belongs to [-2,2], the transformation isn’t 1-1, I get all that. But when the transformation is 1-1, and x belongs to (2,3], why…
AP _
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Analytical analysis to find distributions

I have a Binary Erasure channel. The channel matrix is given as follows: P(Y=0|X=0) = p, P(Y=0|X=1) = 1-p, P(Y=1|X=0) = 1-p, P(Y=1|X=1) = p. Is there any "analytical" way to find possible distributions P' such that $||P - P'||_1 \leq \delta$? I was…
Bikas
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Sum of two uniform random variables, what's the bounds for integration?

Consider random variable $X_i$s are independent and identically distributed. We assume that each $X_i$ is uniformly distributed in $[0, 1].$ (a) Find the cdf and pdf for $Z = X1 + X2$. (b) Draw the pdf of $Z$. So for (a), I understand that we should…
Sami
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Dividing 12 distinguishable balls into 10 distinguishable boxes

I've been struggling with this for a while: I have 12 distinguishable balls and 10 distinguishable boxes. I need to find the probability that there are no cases in which there are boxes with exactly 4 balls in a box. So I thought of going at this…
EMA
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Characterization of joint probability density function of independent random variables

Let $f(x,y)$ be a joint probability density function (pdf) of two random variables $X$ and $Y$. To check whether $X$ and $Y$ are independent, we can compute the marginal densities and check if their product equals $f(x,y)$. My question is: Is there…
Martin
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Inverse of a random variable where \Omega =[0,1]

If I have a random variable $$ X:[0,1] \rightarrow \mathbb{R} \quad \text{so that} \quad X(w)=\min\{w,1-w\} , \quad \text{ where } w \in [0,1]$$ The question is to find the inverse of the random variable ,which is as follows : $$…
sara fkh
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Show Convergence in Distribution

Consider the maximum ${U_{(n)}}$ of $n$ simulated uniform (0,1) i.i.d. random variables ${U_1},...,{U_n}$. Show that $n\left( {1 - {U_{(n)}}} \right)$ converges in distribution to a standard exponential distribution with distribution function…
Pedro Alonso
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Convergence (in dist) of a conditional of two random vectors

Suppose $\bar X$ (respectively $ \bar Y$) is an $ R^m$ (resp. $R^n$) valued random vector with density f(.) and g(.). Let $\phi: R^n \rightarrow R^m$ be $C_1$. If X,Y are independent, then show that $(\bar X + \phi(\bar Y ) | \bar Y = \bar a)…
AvHz
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