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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the joint distribution of dependent random variables

Let $X \sim N(\mu_1, \sigma_1)$, $Y \sim N(\mu_2, \sigma_2)$, $Z \sim N(\mu_3, \sigma_3)$. I want to derive a joint distribution for $X/(X+Y+Z)$ and $Y/(X+Y+Z)$. Since two random variables i.e. $X/(X+Y+Z)$ and $Y/(X+Y+Z)$ are dependent, I can not…
user111740
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Concept of Variance

I am curios about the concept of Variance. I try to get the better understanding of the variance by checking extreme cases. $Var(X) = E[(X^2)] - (E[X])^2$ question 1. What does it mean when Variance equals 0. If variance of random variable X equals…
user16168
  • 697
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What sort of distribution should you expect for the total time taken in bullet chess games?

Bullet Chess is a Chess game that is played very rapidly. At the beginning of the game each player gets a timer set to a specific number of minutes that runs down towards zero while it is his move. For the sake of this discussion, let's limit Bullet…
Dargscisyhp
  • 769
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How to continue this problem to find distribution function of $|X-Y|$

The probability density function of $$f(x,y) = \begin{cases} 1/x^2, & \text{if }0 \le x \le a\text{ if }0 \le y \le a \\ 0, & \text{otherwise} \\ \end{cases} $$ How can you prove that $|X-Y|$ and $\min(X,Y)$ have the same distribution function? I…
Ryan
  • 309
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What is the range of values of the random variable $Y = \frac{X - \min(X)}{\max(X)-\min(X)}$?

Suppose $X$ is an arbitrary numeric random variable. Define the variable $Y$ as $$Y=\frac{X-\min(X)}{\max(X)-\min(X)}.$$ Then what is the range of values of $Y$?
Tanuj
  • 31
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Are $X=\sqrt{r}\cos(\theta) $ and $Y=\sqrt{r}\sin(\theta)$ independent? where $\theta \sim U(0,2 \pi)$ and $r\sim \chi^2_n$

Let $\theta \sim U(0,2\pi)$ and $r\sim \chi^2_n$(Chi square distribution with n degrees of freedom) be independent and define \begin{eqnarray} X=\sqrt{r}\,\cos \theta\\ Y=\sqrt{r}\,\sin \theta. \end{eqnarray} Are $X$ and $Y$ independent? For $n=2$…
Masoud
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Is there a distribution such that sum of its iid variables have uniform distribution?

This question occurred when thinking about the thundering herd problem so I could somehow generate random delays to make load on a server more uniform instead of a big spike when a large number of requests is generated at the same time. Is there an…
Baczek
  • 131
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Find cumulative distribution function of two independent exponential random variables $X$ and $Y$

Let $X$ and $Y$ be independent exponential random variable with rates $\lambda_1$, $\lambda_2$, respectively. What is the cumulative distribution function of $\frac{X}{Y}$? I know that the joint density function is $f(x,y) = (\lambda_1…
user59036
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To find the probability density function

I have done this problem in two ways and I get two different answer.Which one is correct. I provided the link to the image below. https://drive.google.com/file/d/1acToL8QBVq05mTQ9t7TgHgedremJdydA/view?usp=drivesdk For the probability density…
user218102
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What is the probability distribution after interpolation?

Suppose I sample $n$ (some number) numbers from a Normal distribution with zero mean and standard deviation $\sigma$. That is, from $\mathcal{N}(0,\sigma)$. We will call this list of numbers $L$. We will take $L(i)$ to mean the $i$th element of…
K L
  • 123
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Expected value of product of maximum, minimum of n U[0,1] variables

Monte Carlo simulation suggests that this expected value is $\frac{1}{n+2}$. I'm trying to prove this - brute force calculating doesn't work well, does anyone have any tips on how to proceed?
ringwraith10
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Is my professor wrong about this CDF?

Assume the following two facts: $x$ is distributed uniformly on $[-1,2]$. Two variables, $s_1$ and $s_2$ are distributed uniformly on $[x-0.1,x+0.1]$, and $s_1, s_2$ are mutually independent conditional on $x$. Suppose that some $s_1\in[0,1]$ is…
user152497
  • 73
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Random Exponential-like Distribution

Note: Not good at math and my terminology may be very wrong. I have a uniform random number generator that outputs a number between [0,1]. I'd like a function that returns a random number between 0 and 1 using an exponential or exponential-like…
Derek Dahmer
  • 132
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What is the "equivalent" of Gaussian distribution on a segment and on a circle

Does there exist a probability density distribution function with analogous properties to those of the Gaussian distribution, but defined on domains such as: a limited segment $$x \in [a,b]$$ a circular domain (a domain which "wraps…
politopo
  • 123
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Geometric Distribution problem

Home work assignment i'm struggling with , i've been on this for an hour and have nothing : Let $X_1, \ldots X_n$ be a group of independent variables with geometric distribution: $X_i \sim \operatorname{Geom}(p_i)$. Let $Y = \min \{X_1 , \ldots ,…
oopsi
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