# Tagged Questions

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### Lost a factor while integrating by substitution

In the article this article by Rusell May on a generalisation of the coupon collector's problem the integral (5) is simplified in a special case, resulting in the equation (7). At this point, $L$ is ...
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### Integral / Gamma Expectation

I would like to solve the following integral, $\int_{0}^{\infty}\frac{\phi}{a+b\phi} \phi^{c-1}e^{-d\phi}d\phi$. Note $\phi \sim Ga(c,d)$ is a gamma distributed random variable and the integral can ...
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### Marginal change in the expected value

Given the function $$\mathbb{E}[u(t,s,x)]=\int_{X}\max_{t}\left\{ \int_{a}^{b}u(t,s)f(s\mid x)ds\right\} f(x)dx$$ where $f()$ is the pdf, and $X$ is the sample space of $x$. How can i analyze ...
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### moment generating function of a shot noise process

A general setting shot noise process $X(\tau)=\sum \limits_k Z(\tau, T_k)$ where $T_k$ Poisson process with intensity $\lambda(t)$, $Z(.,t)$ independent stochastic processes. Show that the moment ...
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### Weird question about probability density function

I'm assuming "actual" means the total probability of the PDF (the integral from $-\infty to \infty$) must be 1, so $$\int\limits_{-\infty}^{\infty} ke^{-0.1t}dt = 1$$ Wolfram Alpha seems to be ...
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