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23 views

Integral of a non-linear step function on closed interval

I need to compute the following integral for a random variable $a$ with known support and CDF: \begin{equation} \int_{a^L}^{a^H} \left( \sum_{j=1}^{N} \begin{cases} B_j a \mbox{ if } a \leq a_j^*\\ 0 ...
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387 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 ...