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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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Irrational expected value with rational definitions

Is there some probability distribution that can be implemented/defined/etc. without irrational numbers such that it returns 1 an irrational proportion $P$ of the time and 0 the rest of the time, for any irrational probability $P$? If not, for what…
Fricative Melon
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Name for probability density function supported on a closed interval and increasing

I am looking for names/examples/references for probability density functions which are supported on a closed interval, say $[0,1]$, and increasing there. If $f(x)$ is positive and increasing on $[a,b]$ and $I=\int_a^b f(x)dx$ then $g=f/I$ would do…
Maesumi
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Sum of independent exponential distributions?

A person has $100$ light bulbs whose lifetimes are independent exponentials with mean $5$ hours. The bulbs are used one at a time, with a failed bulb being replaced immediately by a new one. (a) Approximate the probability that there is still a…
user3904534
  • 127
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Derive probability density function from joint density function.

I have the following problem. Let $(X,Y)$ be a random vector with joint density function $f(x,y)=8xy$ for $0
HeMan
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Distribution of sum of two directions on hemisphere?

I previously asked the following question: Is average of two random directions also a random direction? Apparently the answer is no, so as a follow up question I would like to find an expression for the distribution of directions as a function of…
Andreas Brinck
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exponential distribution involving customers

Customers arrive at a certain shop according to a poisson process at the rate of $20$ customers per hour. what is the probability that the shop keeper will have to wait more than $5$ minutes (after opening) for the arrival of the first…
Caddy Heron
  • 1,249
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Linear Projection Property for a Logconcave CDF Class

I am an engineering student, new to this forum, and hope I can benefit from your knowledge. I am no mathematician and am really stuck with this problem. I hope someone can help me out. Logconcavity of probabilities is often defined based on the…
F.Farid
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Difference between two $U(0,1)$

Problem: Person $X$ and $Y$ are having a meeting. Person $X$ arrives at a meeting somewhere between $9$ and $10$, the arrival time is uniformly distributed. Person $Y$ arrives at a meeting somewhere between $9$ and $10$, the arrival time is…
jacob
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CDF function formed by vertices.

Below is the problem: Choose a point uniformly at random from the triangle with vertices (0,0), (0, 30), and (20, 30). Let (X, Y ) be the coordinates of the chosen point. (a) Find the cumulative distribution function of X. (b) Use part (a) to find…
Cheul Hee Jason Yoo
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Multivariate Normal from 3 transformed standard normal variables

I have three standard normal variables, $X_1$, $X_2$, and $X_3 \sim N(0,1)$. Let $Y_1 = X_1 - X_2$, $Y_2 = X_3 - \bar X_2$, $Y_3 = \bar X_3$ Where $\bar X_2 = (X_1 + X_2)/2$ and $\bar X_3$ is found in the same way. Show that $Y_1$, $Y_2$, $Y_3$ have…
Stephen
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Is it possible to find a Beta Probability Distribution from two of its percentiles?

In other words, given $x_1$, $x_2$, $p_1$ and $p_2$ in the interval $(0,1)$, is there any algorithm to find $\alpha$ and $\beta$ such that $F(x_i)=p_i$ for $i = 1,2$? Here $F$ is the (cumulative) distribution function associated to the Beta…
Leandro Caniglia
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Distribution function technique - check my approach?

so I'm learning a new topic and am a bit new to probability, so please excuse my elementary question. Given a random sample on an exponential distribution with mean $\theta$ of $X_1,X_2,...,X_n$, let $Y = \ln{X}$. Find the mean of $Y$. We are also…
LearningMath
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Proving that the variance is non-negative

$$(E(X))^2 = \left( \int_{-\infty}^{+\infty}xf(x) \, dx \right)^2 \le \int_{-\infty}^{+\infty}x^2(f(x))^2 \, dx \le \int_{-\infty}^{+\infty} x^2f(x) \, dx = E(X^2)$$ Because of cauchy-schwarz inequality and $f(x) \le 1$. Is my solution correct?
George
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Weighted sum of identical distributed random variables

Suppose $X_1$, $X_2$, $\ldots$ ,$X_N$ are identically distributed (not necessarily independent). Then, given $a_1+a_2+\ldots+a_N=1$, and let $S=a_1 X_1 + a_2 X_2 + \ldots + a_N X_N$. Does $S$ follow the same distribution as $X$?
Jie Wei
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Reconstruct multivariate binary distribution from marginals

I'm have a random vector $\bf a$ with binary entries, $a_i \in \{0,1\}$. The probability distribution $P({\bf a})$ is not fully specified, but I have the marginals $p_i$, which are the probabilities that the $i$-th entry is 1. Additionally, I also…
David Zwicker
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