New answers tagged density-function
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How to solve this question about the beta distribution in a Bayesian analysis?
Let's re-write some of your code to make this a little easier to solve. First, note that the beta distribution can be re-parameterized in terms of $\mu$, its mean, and $\kappa$, a parameter which ...
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Expected Value for Complex-Valued Random Variable
Write $e^{i\theta}$ as $\cos(\theta) + i \sin(\theta):$
\begin{align*}
E(Y)
&=\int_0^{2\pi}\frac{g\,e^{i\theta}}{2\pi}\,d\theta\\
&=\int_0^{2\pi}\frac{g\,(\cos(\theta)+i\sin(\theta))}{2\pi}\,d\...
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Sum of exponential random variables follows Gamma, confused by the parameters
Exponential distribution is a special case of Gamma distribution. If $X$ is a r.v. and
$X \sim Exp(\lambda) \implies f(x) = \lambda e^{-\lambda x} = \frac{\lambda^1}{\Gamma(1)} x^{1-1}e^{-\lambda x}=\...
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