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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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How do you find the smallest set of that represents a distribution of items?

I want to find the smallest set that represents a distribution of items. Say I have the following items with distributions: A: 25% B: 25% C: 50% The smallest set that accurately represents this distribution is the following: [A,B,C,C] That's easy…
George Edward Shaw IV
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Can the company expect to make a profit in the long term?

A company makes cellular phones. One out of every $25$ phones are faulty, but the company doesn’t know which phones are faulty until a customer complains. Suppose the company makes a $ \$ 30$ profit on the sale of any working phone but loses $ \$…
user784928
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Subtracting the minimum from Independent Normal Distributions

Say we pick $n$ independent identically distributee variables $x_i \sim N(0,\sigma^2)$. Say we generated a new series of random variable $X_i = x_i-\min_jx_j$ What is the probability distribution of the $X_i$ NOT equal to zero (i.e. the $X_i$…
Breaking Bioinformatics
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Conditional distribution of $X$ given max$\{X,Y\}$

Let $X$ and $Y$ be independent and both have distribution $F$. Suppose that $F$ has density $f$ wrt Lebesgue measure. Let: $Z\doteq\text{max}\{X,Y\}$ The distribution function of $Z$ is $F^{2}(z)$, and moreover $Z$ has density $f_{Z}(z)=2F(z)f(z)$,…
gva
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Joint probability distribution discrete random variables. Marginal distribution.

Let X and Y be discrete random variables with joint probability mass function; P(X = x,Y = y) = 2x + y/12 , for (x,y) = (0,1),(0,2),(1,2),(1,3) 0, elsewhere Determine the marginal probability function of X and show that it is a probability…
David Gbadam
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"Skew" in data, correct definition

In mathematics, skew refers to the difference between the mean and the median of the data. This means that A = [1000, 1000, 1000, 1000] and B = [10, 1000, 1000, 10] are both NOT skewed. In the field of data streaming skew ofter refers to the data…
MrAkroMenToS
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Discrete Cumulative Probability Distribution

Given F(x) = P(X <= x) for a discrete random variable which of the following is generally true $P(a <= X <= b) = F(b) - F(a), P(a < X < b) = F(b) - F(a), P(a <= X < b) = F(b) - F(a), P(a < X <= b) = F(b) - F(a)$
Muhammad Arfeen
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Sampling Distribution Chi-squard.

In the answer to the question I don't understand something, if someone could help me understand.Proof of $\frac{(n-1)S^2}{\sigma^2} \backsim \chi^2_{n-1}$ . Why in the first answer (−/(/√n))^2 does it have distribution 2(1)?
Javier Andres Marino Villalba
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Probability of $\Pr \left( {\frac{{X + c}}{Y} \le t} \right)$ where $X,Y$ are exponential rv with parameters ${\lambda _1},{\lambda _2}$?

Need to calculate $\Pr \left( {\frac{{X + c}}{Y} \le t} \right)$ where $c>0$ My attemp of solving this probability was $\Pr \left( {\frac{{X + c}}{Y} \le t} \right) = \Pr \left( {X \le tY - c} \right) = \int_{y = 0}^{y = \infty } {\Pr \left(…
Tuong Nguyen Minh
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Inverse probability function to Cumulative probability function

I have looked at how to calculate Inverse Probability Functions from Cumulative Probability Functions, and am familiar with the concept that they are . . . well, inverses. However, I get stuck in actually inverting them. My question is, given the…
Trenly
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Transformations of the uniform distribution

I have a question. T has a uniform distribution in $(0,1)$. Then I perform some operations on T and I get a new distribution. How can I find the new distribution if I know the operations? Is there some kind of formula?
Sommerfugl
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Given joint density of ${(X, Y)}$, how to prove that ${X}$ and ${Y}$ are Gaussian random variables.

Assume that ${(X, Y)}$ has joint density ${ c e^{-(1+ x^{2})(1+ y^{2} ) } }$, where ${ c }$ is properly given. How can we prove that ${X}$ and ${Y}$ are Gaussian random variables, but that ${(X, Y)}$ is not a Gaussian vector.
FrankZ
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The joint distribution of two independent random variables

I have difficulty visualizing what a joint pdf of two independent random variables might look like. The one that I can think of is a cylindrical extension of a univariate Gaussian (let's say extent from x to y). However, in this case, only X is…
Sam
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What is the expected value E(C) that the insurance company is expected to pay?

Discrete probability When all factors are taken into account, an insurance company estimates that the probability of the owners’ of certain house making a claim for $\$5000$ is $0.1$. Furthermore the company estimates the probability of a…
Linda
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How to find $P(W \le w)$ for $W=XY$ knowing the following

Given the joint PDF for $(X,Y)$ $$ p(x, y)=\left\{\begin{array}{cl} \frac{6}{5}\left(x+y^{2}\right) & \text { for } 0
Sorry
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