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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PDF of $\sin(2\pi X)$ where $X$ is uniform random variable

Let $X$ be a continuous random variable with uniform distribution between $0$ and $1$. Compute the distribution of $Y = \sin(2\pi X)$. $\sin(2\pi \cdot0)$ and $\sin(2\pi \cdot1) =0$. So, the inverse image of the function has multiple roots. How can…
Christy
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Distribution of summation of N i.i.d. random variables

I wish to find the distribution of $Y=\sum_{n=1}^{N}\frac{1}{X_{n}^{\alpha}}$, where $\alpha$ is a positive number, and $X_n$ has following distribution: \begin{equation} f_{X_n}(x)=\frac{2x}{R^2}, \ \ \ H\leq x\leq…
Y. Han
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The Expected Value of the number of people, out of 20, who are randomly assigned 2 numbers from 1-20, where their sum is 20

I have been scratching my head over this and I can't see to figure out the exact numbers to use for this problem. The question is as stated: "The numbers 1, 2, . . . , 20 are assigned at random to 10 people so that each one gets two numbers. A…
Mike Campbell
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Probability using integration

A cloth of $10$ meter is to be randomly distributed among $3$ brothers. Find the probability that no one can get more than $4$ meter. (Cloth may be distributed as $3.5$m, $3.5$m and $3$m. Or $3.2$m, $3.8$m and $3$m)
zaki
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Find variance of a sample X and Y

I've taking a test and got fail in this exercise. It says: "Let $X_1,X_2,X_3$ and $X_4$ be independent, identically distributed random variables such taht each of them has a normal distribution with mean 0 and variance 1. We have $Y_1,Y_2$ and $Y_3$…
NabbKitha
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Approximating Poisson Probabilities

I have a random variable X with Poisson distribution with mean 38. I have to find the value that give the approximate value of the probability that is obtained using the central limit theorem with a continuity correction for: $$ P(35 \leq X <…
VP.
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Gamma distribution Confusion

Gamma distribution with respect to the Poisson distribution defined by: $$P(N=n|\Lambda= \lambda)=\frac{e^{-\lambda}\lambda^n}{n!}$$ Suppose that $\Lambda$ has a scale parameter $\alpha$ and shape parameter $\beta$, the we have the probability…
Aurora Borealis
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Expectation Poisson Distribution

A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and $10,000 for each one thereafter, until the end of the year. The number of…
user60497
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If the number of arrivals is one, is it correct to assume an exponential distribution?

The number of arrivals in time in each of my sample is one. Each arrival time is relative to another independent time event for normalization. If the number of arrivals is more than one, the inter-arrival time could be modeled by a homogenous…
user60485
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Reference on Random Variables and Common Operators

I have statistical variables whose values are real and follow gamma distributions. However, the distributions of each of those variables have a different mean and shape parameter. I want to know what would be the distribution of a weighted mean of…
Castim
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When can we directly invert the function across the inequality sign?

I am new to this site. I would like to ask when can we invert the function in the inequality? Question: Let X be a continuous random variable with pdf . Suppose () is strictly monotonic, differentiable function of x. The random variable =() has the…
user590977
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conditional probability in sum of two Poisson RVs.

Here we go ..... Serious accidents in a manufacturing factory are modeled by a Poisson distribution with a mean rate of 1.6 per week. What is the probability that in a four week period, there is exactly one week in which there are serious…
Waitara Mburu
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Let $X$ and $Y$ be two Poisson random variables with same lambda parameter. What is the distribution of $\frac{X}{X+Y}$?

Let $X$ and $Y$ be two Poisson random variables with same lambda parameter. What is the distribution of $\frac{X}{X+Y}$? I know it is distributed uniformly between $[0,1]$, but i couldn't prove it. Can you help please?
user60167
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What is this probability distribution.?

There are two variables $a$ and $b$. (The first value of variables : $a=1,b=0$) We will add $1$ to $a$ or $b$ for $n$ times. ($n \in \mathbb N$) The probability of adding to each variables are : $$P_a = k({a \over a+b})+(1-k)({b \over a+b})$$ $$P_b…
sunghwa Kang
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Distribution function of $X_1 + X_2$ given probability distributions of $X_1$ and $X_2$

Suppose I have a probability distribution for random variable $X_1$ given by: $$ P(x) = \begin{cases} 1/a, & \text{if} \;\; 0 \leq x \leq a\\ 0, & \text{otherwise} \end{cases} $$ and $X_2$ with probability distribution: $$ P(x) = \begin{cases} 1/b,…
Truth-seek
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