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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If$ X\sim N(\mu,\sigma^2),Y\sim N(X,\tau^2)$, how can I know the distrubution of $Y$?

It seems to be a simple computation of condiontional distrubution function.But when I really work it out: \begin{align*} P(Y\leq y)&=\int^{\infty}_{-\infty} f_X(x)P(Y\leq y|X=x) \mathrm{d}x\\ &=\int^{\infty}_{-\infty}\int^y_{-\infty}…
Egyptian
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Is there a maximally skewed bounded distribution?

Among all bounded random variable $X$ in $\mathbb{R}$ such that $|X -\mu_X| \leq B$ for some $B>0$, one with the maximum variance has mass $1/2$ at $B$ and $-B$ each. Is there also a construction for the bounded RV with maximal skewness $(E[(X -…
gwtw14
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Weighted sum of random variables

Maybe this question is a little bit strange, but actually, I can't handle it. Suppose we have a random variable $Z$ which is equal to random variable $X$ with probability $p$ and is equal to random variable $Y$ with probability $q$. Can i write…
Optimized Life
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PDF and CDF distribution looking for feedback on my work

Given $$X_i ∼ Uniform[0, 1] $$for $$i = 1, .., n.$$ What is the distribution of $$M := min(X_1, ...., X_n)?$$ You may assume that $$X_1,X_2, ... ,X_n are independent.$$ My solution: $$X_1 ∼U [0,1]$$ $$PDF f(x)=1, 0≤ x≤ 1$$ $$ F(x)= \int_0^{x}…
user29
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Find the mean cost of maintenance in the first year of purchase of the machine.

A sewing machine within first year of its purchase requires $X$ number of inspection visit by a maintenance technician and $X$ follows a poisson distribution with $\mu=4$ (i) First visit is free of charge and subsequent visit costs $1000$ each.…
Alhabud
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Cumulative probability distribution that better fits data plot

I obtained this cumulative probability density plot of my data. I tried normal distribution but found that it underestimates lower values between 2 to 6. Is there a probability distribution that better fits such a data plot?
Sun Bear
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Convergence of random variables defined by the normal distribution.

I'm trying to prove this: Given $\{\mu_n\}$ and $\{\sigma_n\}$ sequences of real numbers such that $\mu_n \rightarrow \mu$ and $\sigma_n \rightarrow \sigma$, if $X_n \sim N(\mu_n, \sigma_n^2)$ and $X \sim N(\mu_n, \sigma_n^2)$ then $X_n…
balaya
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Is there a distance measure between probability distributions to measure if one is a subset of the other

I’ve two discrete distributions, say $p$, $q$. I am looking for a distance measure (need not be a metric, something like KL divergence is also fine) that satisfies the following: If support of $q$ is a subset of support of $p$, then the distance…
Nagabhushan S N
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Bernoulli process failures rate

I have seen an unproved claim, which states that given an infinite Bernoulli process with probability $p$ of success, for every $c
AlexTren
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What distribution describes the locations of traffic signals?

I am working on a simulation that places radio unit at traffic signals, is there any way to generate locations of traffic signals that make the simulation realistic? Lets say we have 200 × 200 m area in a commercial block in a city. what is the best…
Alaa
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What is the probability distribution for the maximum number of occurrences of a repeated simple trial?

Let's say I have a normal, unbiased 6-sided die and I roll it 100 times. Some number is going to get rolled the same number or more often than any other number. What is the probability distribution and expected value for the number of times that…
DDub
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How do I make the sum of n random independent numbers uniform?

I've looked around for a bit, and found that this is to do with the Irwin-Hall distribution, however I don't know anything about calculus/statistics, could someone explain to me in baby terms how I would go about making the sum of n random numbers…
matidfk
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Basic discrete probability

This is a very basic question in probability, but I would like a rigorous answer nevertheless. When a text describes a random experiment, say, "With probability $p$ we assign $0$ to $x_1$, and otherwise we assign $1$, and independently with…
Jack
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How to calculate the mathematical expectation of a function?

Suppose that $T$ is a random variable, $F(T)$ the function of random variables. How can I compute the expectation of a function of random variables if the probability density function (PDF) $g(t)$ for $T$ is given?
Yang
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Method of moment estimator Pareto

I'm working on a Pareto distribution function, where I have to find the method of moments estimate of $\theta$. The function is: $f(x|x_0, \theta) = \theta \cdot x^{\theta}_0 \cdot x^{-\theta-1}$ When $x > x_0$ and $\theta > 1$. Assume that $x_0 >…
bestmate21
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