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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probability and series

$X$ is a discrete random variable taking on the values $X=1,3,3^2,3^3,\ldots,3^m$ and $f(x)=P(X=x)=c / x$ for a constant $c$. Find $c$. Solution: Since $P(X)=1$, we know that $cx=1$, so $c=x$. To find $x$, we have $x=\sum_{k=0}^m 3^m$. Since this…
John
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characteristic function problem 4

which of the following is not a characteristic function? a) 1 b) $e^{it} $ , $t \in R$ c) $\frac{1}{1-it} $, $t\in R$ d)$e^{|-t|}$, $t \in R$
user157012
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Sample mean of gamma distribution

I would really appreciate help on this homework problem. The random variable X is the waiting time till the occurrence of the first event in a poisson process with expected waiting time beta = .7. Consider a sample of size N = 40 from X. a) find…
user87654321
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probability mass function of a random pick from either of the other two random entities.

This is not a hypothesis testing problem. Let $Z$ be discrete non-negative random variable, such that it picks either the value of random variable $X$ with probability $p$ or the random variable $Y$ with probability $q$. The pdfs of both $X$ and $Y$…
kaka
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Multinomial Distribution- expected number

Suppose you have a box with five balls of different colors. If you draw a ball 100 times and replace it, what is the expected number of different colors you would have after 100 trials?
rezzz
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Bernoulli trials with at least 1 success and 1 failure

Independent Bernoulli trials are performed, with probability $1/2$ of success, until there has been at least one success. Find the PMF of the number of trials performed. How is this different from the negative binomial?
helpwithquestion111
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The size of a fish in a lake follows a normal distribution

I have a homework question that I wasn't positive about. This is the first probability course I have taken and the class is only taught using excel so I apologize for the lack of formulas in my reasoning. The size of a fish in a lake follows a…
user87654321
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Lifetime of light bulbs is modeled as a Poisson Process - using excel

I have a homework question that I can't seem to figure out. Any help is appreciated! The lifetime of light bulbs (in days) is modeled as a Poisson Process with expected lifetime of beta = 200 days. A certain building has 1,800 bulbs. What is the…
user87654321
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Probability involving 3 standard normal random variables

If $X,Y,Z$ are independent standard normal random variables, compute $P(3X+2Y<6Z-7)$. One way is to evaluate $$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{(6z-2y-7)/3}\frac{\exp(-(x^2+y^2+z^2)/2)}{2\pi\sqrt{2\pi}}dxdydz.$$…
graidym
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probability density functions and cumulative distribution function

Suppose $X$ is an absolutely continuous real random variable, (that is, there exist a non-negative integrable function $f$, such that $\int_\mathbb{R} f=1$ and for every interval $I\subseteq \mathbb{R}$, $\int_I f = P(X \in I)$, such $f$ is called a…
Angelo Russo
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Operations with probability distributions

I had an idea that passes by declaring a new type of computer variable (like Integer, Double, etc.) that represents a statistical probability distribution (PDF), for that I would need to define the basic operations; sum, multiplication, inverse and…
Santi Peñate-Vera
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Probability distribution of $M_n = min(X_1 ... X_n)$

I want to derive the distribution of $M_n=min(X_1 ... X_n)$ in another way than by a combinatorial analysis. Say we have $X_1...X_n$ represent $n$ draws without replacement from the numbers $1...N$ with equal equality. First, I want to compute:…
iJup
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Minimum of the sample size estimator Bernoulli distribution

Given is a random sample $X_1 ... X_n$ from a $Ber(p)$ distribution. Consider the estimator $T = min\{X_1 ... X_n\}$. First, what is now the distribution of $T$? The minimum says that everything should be working ($X=1$), so I think $T $~…
iJup
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Expected value of a random variable and its square root

Can the expectation of a random variable be written in this fashion: $$E(\sqrt{X} + X) = E(\sqrt{X}) + E(X)$$ Thanks in advance
Joz
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Distribute items with exaggerated coeficient

As you can probably tell from the way this is formulated, I am not a mathematician. I'my trying to program something but I'm trying to do it well and I don't want to reinvent the wheel. There must a very well-established way of doing this, but I…
eje211
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