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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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Do these mushroom/hamburger-looking shapes have a name?

I produced the following image using a statistical simulation and am wondering if the resulting shapes have an existing name: (Blue indicates where the field is near zero, green where it is positive, and red where it is negative) These shapes…
CompileYourCake
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Finding Probability using Moment-Generating Function

I am given a moment-generation function $M_x(t)= e^{t+t^2}$ and asked to find the probability that the random variable is greater than $2.5$ Any help would be greatly appreciated!
user87683
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Find exponential discrete probability distribution where $\sum_n \lambda e^{-\lambda x}= k$

Apologies if the title is not well formatted. First time posting a formula in a title. My issue comes from the following situation. I want to define a probability function by regions so that: $p(x) = \left\{ \begin{array}{ll} \frac{0.4}{10-2} &…
Sergio Pardina
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Exact form of pdf of maximum of normal random variables

$$ z = max(x+b,y) $$ where x ~ N(m1,s1) and y~N(m2,s2), b is a contant What's the pdf of z? Or exact form of E(z)? (E is expectation operator) To the best of my guessing from the literature it is related with Weibull…
user1849133
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Is there any property that captures $F(\alpha x) \geq \beta F(x)$ for $1>\alpha,\beta>0?$

Given a CDF $F:\mathbb{R}_{\geq 0}\to [0,1]$ such that $F(\alpha x) \geq \beta F(x)$ for some $1>\alpha,\beta>0.$ I'm trying to figure out if there is any known family of distributions for which this condition holds. Is this somehow related to…
Tal Alon
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Number of draws required for ensuring 90% of different colors in the urn with large populations

My problem is: An urn contains $10000000$ ($10^7$) different colored balls, namely $K_1, K_2,\dots,K_n (n=10^7)$ with $K_1=1000, K_2=1000,\dots,K_n=1000$. My question is: How many balls do I need to extract to ensure to obtain $90\%$ ($1000000$ or…
Danny Bennett
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Convolution of independent distributions

Let F be a distribution on $R$ and X be a randomvariable with distribution F. If $x\geq0,$ $\overline G(x)=P(X>x|X\geq0)$ (i.e. conditional distribution), then $\overline{G*G}(x)=P(X_1+X_2>x|X_1\geq0,X_2\geq0).$ Here, $X_1$ and $X_2$ are two…
user86349
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Holder norm of Wiener process

Show that if $W(t),\ 0 \le t \le 1$\ is a standard Wiener process, then its Holder norm $\sup\limits_{0 \le s,\ t \le 1}\frac{|W(t) - W(s)|}{|t - s|^{\alpha}},\ 0 < \alpha < \frac{1}{2}$\ has moments of all orders. Does the moment generating…
user72118
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Random vector with uniform distribution.

Let $(X,Y)$ be a random vector with uniform distribution at $0 \leq x \leq 1$, $x \leq y \leq x+h$ with $0
Cure
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Probability distribution of defective parts

Suppose there are 1 million parts which have 1% defective parts i.e 1 million parts have 10000 defective parts. Now suppose we are taking different sample sizes from 1 million like 10%, 30%, 50%, 70%, 90% of 1 million parts and we need to calculate…
irum
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The method reducing the distance between CDF by sampled score function

Let's $p_\theta(x)$ is parameterized PDF, $P_\theta(x)$ is CDF of $p_\theta(x)$ and we know the distribution. $q(x)$ is also PDF and $Q(x)$ is CDF of $q(x)$ but we only get the sample of score function(I mean unnormalized value $q(x)={1 \over…
김한결
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Can we figure out a distribution function for how long does it take for the following system to terminate?

Suppose we simulate the following system: In the beginning there are $N$ robots and a large reserve of fuel: $T$ units of fuel in total. Each robot takes some amount of fuel to start out. They consume fuel at a constant rate: 1 unit / second -…
Tom
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Distribution of $ Y_i=\frac{X_i}{X_1+X_2+...+X_n}, i=1, 2, ..., n-1 $ where $X_1, X_2, ..., X_n$ are iid each with a standard exponential distribution

Problem Let $X_1 ;X_2;...;X_n$ denote independent distributed random variables, each with a standard exponential distribution. Let $$ Y_i=\frac{X_i}{X_1+X_2+...+X_n}, i=1, 2, ..., n-1 $$ Show that the distribution of $Y_1; Y_2;...; Y_{n-1}$ is…
João Castro
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Convergence issue calculating a conditional distribution from the joint

I want to find the probability of $P(X<0.5 \;|\; Y>0.25)$ of a joint pdf $$f_{(X,Y)}(x,y)= \frac 1 x $$ with $00.25)=\frac{P(X<0.5 \;,\; Y>0.25)}{P(Y>0.25)}$$ The denominator can be calculated…
JAP
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Given the PDF of $X$ which is right hand continuous, compute PDF of $Y$ = CDF$(x)$

Let x have a piecewise right hand continuous pdf, $f_X(x)$, which is defined as follows. $$f_X(x) = \begin{cases} \frac{1}{2}(x+2)^2 & -2 \leq x < -1 \\ -\frac{1}{2}x +\frac{1}{12}\delta (x+1) & -1 \leq x < 0 \\ \frac{1}{2}x & 0 \leq x < 1…
Farhood ET
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