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.

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Using CLT to approximate probabilities

Question: An analysis of economic data shows that the annual income of a randomly chosen person from country A has a mean of 18,000 and a standard deviation of 6,000, and the annual income of a randomly chosen person from country B has a mean of…
user118342
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Dense Subset of $L^{2n}$ for Range of the distribution

I am selecting a distribution for MIT-BIH arrhythmia data that is ECG data which follows AAMI standards. Let distribution $A$ : $D(\mathbb{R}) \subset L^{2}(\mathbb{R})$ such that \begin{equation} A : D(\mathbb{R}) \to L^{2}(\mathbb{R} \times…
Léo Léopold Hertz 준영
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Find the probability distribution function

Let $X$ and $Y$ be random variables such that $Y|X = x$ is $\text{Exp}(1/x)$ and X is $\text{Gamma}(2,1)$ find the pdf of $Y$ and $E(Y)$
jack
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probability function for poisson random variable

A poisson random variable has a mean of x=6.25. A random sample of this variable is drawn. What is the probability function for sum S = $\sum_{i=1}^n X_i$, as specifically as possible. I have no idea how to attack this.
Nick
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Determine a joint probability density function

So I don't really understand joint probability density functions. I've read that the joint density is the derivative of the joint probability function, but I don't understand what to do with the double integral of the density. The function is…
Nick
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The minimum value of a uniform multinomial distribution

Suppose that $n$ balls are randomly put in $k$ boxes, with uniform chance; called the uniform multinomial distribution. I'm interested in the chance that no box is empty. In other words, the chance that the minimum number of balls in any box is…
user44090
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Cumulative distribution function changes variable

I am really at a loss for what this question is even asking. Could someone please explain it to me? Suppose continuous random variable X has the cumulative distribution function F(x). Find the CDF G(y) for random variable Y = F(X). Provide all…
Nick
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Calculating f(x) for an i.i.d.

We know that for a gaussian distribution, $f(x) = 1/\sqrt{2\pi\sigma^2} \exp[ -(x-\mu)^2/2\sigma^2 ]$ I was wondering that given an i.i.d. random variable with a given distribution, whether there exists some function $f(x)$. For e.g: Let us say, $X$…
Rohit
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Laplace distribution from uniform distrubtion

Since I'm interested in the simulation of probability distributions on the computer. I want to simulate the Laplace distribution. When I was looking on the laplace distribution wikipedia page…
Krasdo
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Find $P(T>t)$ and thus find the cdf for $T$ - exponential distribution

I have a word problem question where a "man" is waiting for two buses, bus A or bus B. Let $T_1(T_2)$ be the time till the next bus A(B) arrives. $T_1$ and $T_2$ are independent continuous variables. They can be defined as…
Krish
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Probability - rolling two dices and flipping one coin two times

Two six sided fair dice are rolling. If sum of fallen numbers is less than $5$, than coin is flipping two times. Random variable $X$ represents sum of fallen numbers, $Y$ represents number of fallen tails. Find distribution of random variable $(X,…
user2982390
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Sampling distribution of sample mean and sample variance

Let $X_1, X_2, \cdots, X_n$ be an identical and independently distributed sample from $N(\mu, \sigma^2)$, define: $$D = \frac{1}{t}\left[\overline{X} + \frac{1-\rho}{2} S^2\right]$$ where: $t$ and $p$ are fixed constants $\overline{X} =…
Trts
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what is the cumulative distribution function of a logistic function?

I've found on wikipedia for Logistic function (http://en.wikipedia.org/wiki/Logistic_function) they have the formula for a Logistic curve: $P(t) = 1 / (1 + e^{-t})$ and they have a diagram of the curve. What is the formula for the cumulative…
d l
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An urn initially contains r red and g green balls. A ball is chosen at random from the balls find the marginal probability

An urn initially contains $r$ red and $g$ green balls. A ball is chosen at random from the balls in the urn and its colour is noted. Then it, together with $c > 0$ balls of the same colour as the drawn ball, are added to the urn. The procedure is…
Kasun Jayasuriya
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Joint density function properties

here are the properties of the joint density function, can someone explain me the 4° point? (it says: for every... as a point of continuity of f)
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