2
votes
1answer
102 views

Weighted integral of random variables

Given a random zero-mean gaussian random variable $X(t)$ with parameter $t$, such that $E [X(t) X(t^\prime)] = \sigma^2 (t) \delta_{tt^\prime}$, is it possible to produce a single gaussian random ...
0
votes
0answers
355 views

Integral of a gaussian with random variance

Assuming: $$X(x,\mu)=\frac{1}{\sqrt{(2\pi)\sigma^2}} \exp[-\frac{1}{2}\frac{(x-\mu)^2}{\sigma^2}]$$ the integral of $X(x,\mu)$ from $-\infty$ to $+\infty$ is: $$S=\int_{-\infty}^{+\infty}dx ...
2
votes
2answers
181 views

Integral of a random function

How is it possible to evaluate the integral: $$I(\mu,\sigma)=\int_0^{2\pi}\sin(\omega t)^2dt$$ where $\omega$ is a random variable having a normal distribution $N(\mu,\sigma)$? What is the $pdf$ of ...