# Tagged Questions

Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

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### Probability Density Function Example Help

I am reading through the text, "Introduction to Probability Theory with Contemporary Applications" by Lester Helms. I am stuck on the attached example. I understand how the author obtained the joint ...
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### Polynomial Chaos with Beta Distribution - Standard Beta Random Variable, Transformation of Beta Random Variable

Background: I am dealing with a non-intrusive polynomial chaos expansion (e.g. here [Hosder,Walters;2010]). This means I want to represent an uncertain output $U(\xi)$, dependent on a vector of ...
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### compound probability and conditional expectation

I'm stuck on a formula which looks obvious but that I fail to prove: If $Z$ is a real-valued random variable with distribution $\mu$, $T_z$ is a random time for each $z\in \mathbb{R}$ and $B$ is a ...
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### Central moments of a Bernoulli distribution

Consider a discrete random variable distributed as a Bernoulli: $$Y=\begin{cases} 1 & \text{with probability } p\\ 0 & \text{with probability } 1-p \end{cases}$$ The $n$-th central moment ...
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### Wishart plus scalar multiple of identity

Is the sum of a Wishart distributed matrix and a scalar multiple of identity matrix, another Wishart distributed matrix? I guess it is not. If not, what is the distribution called and can its density ...