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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Which biased random sources can be obtained from an unbiased one?

Let $X_i$ with $i\in\mathbb N$ be a sequence of independent binary random variables with uniform distribution $\operatorname{Pr}(X_i=1)=\operatorname{Pr}(X_i=0)=0.5$. For $p\in[0,1]$ with $p2^n\in \mathbb N$, it is easy to transform this sequence…
Thomas Klimpel
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Dealing with a geometric distribution

here's a question we got for homework. Please excuse my poor translation. Anyhow: A cellphone company has n1 call users and n2 text users. The probabilities of a user to be connected at a given moment are p1 and p2 accordingly (the…
yotamoo
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probability-distribution that has its mode equal median

Could anyone tell me any asymmetric distribution whose mode=median? Thanks in advance.
monkinsane
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how to compute the probability ditsribution of the average of n iid random variables

It has been a long time since I took a probability class, and I'm sure that this site is for any level of mathematics... Given $n$ iid random variables, I want to compute the pdf of their average. How can I do that? I know I can do for summation but…
Endo
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Waiting time in a bus stop

I have a question in a Probability theory and think that it could be solved by exponential distribution. However I'm not confident for dealing with this. Hope to get some helps. Thanks in advance. A working schedule of buses at a bus stop as…
user
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Probabilty of random number distribution

Given a random number generator generating integer numbers in the range 1 to N. What is the probability that a given number appears Q times (not necessarily sequentially, but in any order) in a sequence of M numbers, ie P1 is the probability that…
Victor
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Combining independent distributions

Suppose that $X_{1} \sim B(n_{1},p_{1})$ and $X_{2} \sim B(n_{2},p_{2})$ are independent. Write down the moment generating function for the random variable $Y=X_{1}+X_{2}$. I know the moment generating function $M_{Y}(t)$ is defined at…
user2850514
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Attention capacity and queue length in a cafeteria

I have not been able to solve this problem. The difficulties I am having are that I don't know if its possible to solve for a numerical value, or if the solution is supposed to be in terms of $t$ (time). In a cafeteria, there is a rate of costumer…
Severo Raz
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How to compute transfomed pdf under non-injective function

I have a two random variables $x,y$ which are both (independently) distributed accordingly to the triangular distribution $x,y \sim Tri(-1,1,0)$ where I used the definition from Wikipedia. Now, I want to calculate the distribution of $z$, with $z =…
bonanza
  • 441
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Get distibution depending on three random variables

Given the function $\text{result} = \frac{a*b}{1-c}$ with 3 independent equally distributed random variables $a$, $b$, and $c$, how do I derive the distribution of $\text{result}$? How can I get the range of the top 20 percent of $\text{result}$? I…
grackkle
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$N$ balls and $M$ boxes, probability of last $ i$ boxes are empty

I encountered this problem. There are $M$ boxes and $N$ balls. Balls are thrown to the boxes randomly with probability of $\frac1M$. The boxes are numbered $1, 2, 3, ..., M$. what is the probability of last $i$ slots are empty, $i = 1, 2, 3,…
robithoh
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Convergence in Probability and Sum of Chi-square

Let $X_n = \frac{1}{n} \sum_{i=1}^{n} Y_i^2 $ where $Y_i$ are standard normals. How do I show that $X_n$ converges to 1 in probability? Does the CLT not imply that $X_n$ converges to a normal(0,2) in distribution? This has been a point of confusion.…
Peter
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problem finding marginal distribution for a PDF

I need to find the marginal distribution function $f_y$ for $$f_{xy}(u,v)= \begin{cases} 1\over u, & \text{$u\ge 1, 0\le v \le {1 \over u}$} \\ 0, & \text{else} \\ \end{cases}$$ my problem is with the domain $1
user107761
  • 381
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Find pdf of $X = 5Z_1 - Z_2$, where $Z_1$, $Z_2$ independent

$$X = 5Z_1 - Z_2,$$ where $Z_1$ and $Z_2$ are independent. Find pdf of $X$. My approach is to find the cdf $\to$ differentiate $\to$ pdf cdf: $$\begin{align}F_X(x) &= P(5Z_1 - Z_2 \le x)\\ &= P(Z_1 \le (X+Z_2)/5)\\ &=…
augee
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Is the inverse of a cdf always also a cdf?

If $F(x)$ is a valid cdf (in that it is increasing from 0 to 1) is $F^{-1}(x)$ also a valid cdf?
Angada
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