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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.

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how to calculate remaining waiting time in exponential distribution?

ABC corp conducted a study of service times at the drive-up window of fast-food restaurants. The average time between placing an order and receiving the order at restaurant is 2.45 minutes. Assume that the waiting time follows exponential…
user269867
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Bounding the moment generating function at $2$ from the expected value and the value at $1$

Let us suppose that $X$ is a random variable with expected value $0$ and whose moment generating function at $1$ is $m_X(1)=z\ge1$. As a function of $z$, what is the smallest possible value of $m_X(2)$?
Brian Jefferson
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Joint PDF to CDF

So I have this joint PDF: $$ f(x,y)= \begin{cases} 4xy & \text{ for } 0 \leq x \leq 1, 0\leq y \leq 1\\ 0 & \text{ otherwise} \end{cases} $$ To make this a CDF, I have tried to double integrate the PDF from $-\infty$ to $x$, $-\infty$ to…
baba
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Coin toss with dynamic probabilities

So, I got a repeated experiment with two outcomes, i.e. a coin toss, but the probabilities might change every toss and are independent. Typically, they might come in sequences of the same probabilities and then change at some point. So, what I want…
user160531
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Cumulative Distribution Function and

The demand, $X$, for a firm’s product is a random variable with density $f(x) = 2x$ for $0 ≤ x ≤ 1$. The corresponding cumulative distribution function is $F (x) = x^2$ for $0 ≤ x ≤ 1$. The firm’s profits, $Y$ , as a function of $X$ are $Y = \sqrt X…
Rosie E
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What is the value of $E[|X|]$?

Let X be a zero mean unit variance Gaussian random variable.What is the value of $E[|X|]$?
user157967
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expectation of random variable

I have this question : What is the expected value of $E(X^{100})$ if X is a random variable such that $E(X)=E(X^2)=1$? I am very confused as $X$ could be a poisson or gamma variate.
user157012
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Conjugated priors (Pareto and Beta): Does this distribution have a name?

$$F_X(x)=\begin{cases} \quad\dfrac{\alpha}{\alpha+\theta}\left(\dfrac x\omega \right)^\theta &\text{ if } x<\omega \\ \\ 1-\dfrac{\theta}{\alpha+\theta}\left(\dfrac\omega x\right)^{\alpha} &\text{ if } x>\omega \end{cases}\quad\text{ where } 0\le…
Sergio Parreiras
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Inverse gamma distribution

Wikipedia (at the time I write this) has two mutually inconsistent entries (one after the other !, http://en.wikipedia.org/wiki/Inverse-gamma_distribution#Properties): $$X \sim \mbox{Gamma}(k, \theta) \Leftrightarrow \dfrac{1}{X} \sim…
Sergio Parreiras
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What is the prefered approach for this? (distribution)

Let's say I want to have a list of random numbers that follow a distribution. All random numbers should be between 0 and 100, and the mean is variable but doesn't change while we generate the randoms. Behavior: The mean = 50, there's the same…
malloc19
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Jump process Calculate integral of Poisson - Help understanding a solution

$N_{t}$ represents Poisson process on filtered probability space. Calculate $ \int \limits_{0}^{t} N_{s-} dN_{s} $ ? I am trying to learn it, and I have the solution but can not understand a step $ = \sum \limits_{0
user669083
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Probability that one folded normal is bigger than another?

What is the probability that one folded normal distribution is bigger than another? In other words, if $Z_1=\mathcal{N}(\mu_1,\sigma_1)$ and $Z_2=\mathcal{N}(\mu_2,\sigma_2)$, what is $\mathcal{P}(|Z_1|>|Z_2|)$?
user21725
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Expectation of a function in Poisson Distribution

Find the expectation of the function $\phi(x) = xe^{-x}$ in a Poisson distribution. My Attempt: If $\lambda$ be the mean of Poisson distribution, then expectation of $$\displaystyle \phi(x)=\sum_{x \mathop \ge 0}…
square_one
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Expectation of Continuous variable.

Given the probability density function $$ f(x) = \begin{cases} \frac{cx}{3}, & 0 \leq x < 3, \\ c, & 3 \leq x \leq 4, \\ 0 & \text{ otherwise} \end{cases} $$ I have found $c$ to be $0.4$ and $E(X)$ to be $2.6$. But I'm being asked to find $E(3X -…
jbbrsh1494
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What is the expectation of $X^2$ where X has a truncated normal distribution?

Suppose that $X\sim N\left(a,\mbox{ }\sigma^{2}\right)$, what is $E\left\{ \left[1\left\{ X>b\right\} \exp\left(X\right)\right]^{2}\right\}$? $b$ is a constant.
user150272
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