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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Adding uniform distributions?

i have a variables X and Y which are discrete, independant and uniformly distributed,$$X\sim[1,5],Y\sim[1,7]$$ I want to derive the variance of $$\frac{(X+Y)}2$$, but I don't know how, any help is much appreciated. Not sure if it helps but $E[X]=3$…
Yep
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what is this probability distribution?1

if $X_1,X_2,X_3,...,X_n$ is a sample size $n$ and $i.i.d.$ of a random variable with distribution $f(x)$, and $$Y=X_1.X_2.X_3.....X_n$$ what is the approximate distribution of $\log{Y/n}$ for large sample (high $n$)? Is not information missing from…
Muradin Bronzebeard
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What probability distribution should I use for this situation?

Supposedly a baker mixes 5000 raisins into a large quantity of dough which he mixes well and bakes 1000 equally sized cookies from. So, I'm going to define a random variable X as number of raisins in a randomly selected cookie. But I'm not sure…
vxs8122
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Tricky pdf proof

How do one go about solving this tricky question: Given the pdf of $k_{o}$ as shown below $$f_{k_{o}}(k)=2\pi v ke^{-\pi v k^{2}}, \quad 0\leq k\leq \infty $$ and $q$ is given as $$ q = \zeta_{o} k_{o}^{n}, \quad 0\leq q\leq q_{u}$$ Prove…
Abdulhameed
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Probability of event on Poisson process arrival

I have the following problem: A mail server, sends emails with rate $7.5/\text{hour}$. What is the probability that it will send exactly $5$ emails in one hour? To solve it, I did the following using a Poisson distribution: $$\frac{7.5^5…
VP.
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Find cdf given pdf.

Let $X$ be the lifetime of a personal computer. Suppose the pdf of $X$ is $$ f_X(x) = \begin{cases}\frac{1}{5}e^{-\frac{1}{5}x} & x > 0 \\ 0 & {\rm otherwise}\end{cases} $$ Assume that costumers replace their computers at failure or three…
Michael
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Find cdf $F(w)$ given $w=g(v)$

For part (a) finding the cdf $F(w)$ of $W$,my way to do it: $F(v)=F(g(v))= \begin{cases} 1/(5 \sqrt{2}) \int_{-\infty}^{-10} e^{-(-10)^2/50}\, dx & \text{$v<-10$} \\ 1/(5 \sqrt{2}) \int_{-10}^{10} e^{-(v)^2/50}\,dx & \text{$-10≤v≤10$}\\ 1/(5…
Michael
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Joint probability distribution table

I am solving a problem in probability related to Joint distribution. Let’s say I am playing shooting arrow at a target and after every shot, I choose a number from {2,5}. I shoot twice and everytime I hit the target, I choose 2 and if I do not I…
Four Seasons
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calculation of Probabilities with two normal distributions

This is the problem I have to solve for a job at school. Can anyone help me, what kind of distributions approximations do I use and how to calculate the requested probabilities? In one factory there are two M1 and M2 machines that produce screws.…
hellsing199111
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Probability mass function with changed variable

I have this task and would love some feedback on whether I'm going in the right direction: Suppose the random variable $X$ has distribution given by probability mass function $$ \begin{array}{c|lcr} x & \text{-2} & \text{0} & \text{2} & …
Jake
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Convergence of CDF

I have a cumulative probability distribution function F(x). I need to prove that $\sum_{n=2}^\infty n(F(x)^{n-1} - F(x)^n)$ does not converge for all $x \in \mathbb{R^+} - \{x:F(x)\ne 0\}$
Andy
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distribution of Poisson random variables

If I have a sample $X = (X_1,...,X_n)$ with Poisson distribution, and I have $Y = n\cdot X_{1:n}$ it has the same distribution with the same parameters or I have to change something?
Johnny
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Find the distribution of U = X/Y

I have the following situation: The joint distribution of X and Y is defined as $$ f_{XY}(x,y) = 2 \mathbb{I}_{(0,y)}(x) \mathbb{I}_{(0,1)}(y) $$ I need to find the distribution of U = X/Y. I tried to find the marginal distribution of X and Y ($X…
Cauchy_96
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$X$ is Gaussian, how to evaluate the joint probability of $X$ and $X^2$?

We assume that $X \sim N(0,1)$ is a Gaussian RV, I wish to evaluate the probability $$\Pr(X^2 \leq 4, X \geq 5)$$ Can I proceed as follows: $\Pr(X^2 \leq 4, X \geq 5) = \Pr(X \geq -2, X \leq 2, X \geq 5) = \int\limits_{-2}^2 f_X(x) dx + …
Olórin
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Probability random variable binomial distribution

Every day, a lecture may be canceled due to inclement weather with probability 0.05. Class cancelations on different days are independent. (a) There are 15 classes left this semester. Compute the probability that at least 4 of them get canceled. (b)…
Satyaki Chatterjee
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