If I have a variable $X$ that has a gamma distribution with parameters $s$ and $\lambda$, what is its momment generating function. I know that it is $\int...

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I'm learning about integration by parts, primarily from Stewart's text (7th edition). In a supplemental book I have it brings up something calle...

Given the following parametric find the distance between the two lines: $x=2+t\;,\;\; y=1+6t\;,\;\; z=2t$ and $x=1+2s\;,\;\; y=6+14s\;,\;\; z=-1+5s$ I tri...

For reference this is from page 27 here Consider the stochastic heat equation $$ \begin{cases} \dfrac{\partial u}{\partial t}(x,t)=\dfrac{\partial ^2 u}{\...

Why is ${n-1 \choose -1} = 0$ when (-1)! is undefined? Shouldn't ${n-1 \choose -1}$ also be undefined?

What is appropriate usage of "numerator", "denominator", and "nominator" to refer to parts of a fraction? I'm posting this question and answer here b...

Use the $\epsilon$,$\delta$-definition of limits to show that $\lim\limits_{x\to a} f(x)=L$ if and only if $\lim\limits_{x \to a^+} f(x)=\lim\limits_{x\to...

$ I = \int (x^2 + 2x)\cos(x) dx $ Integration by Parts, choose $u$: $$\begin{align} u &= \cos(x) \\ dv &= (x^2 + 2x)dx \\ du &= -\sin(x) \\ v ...

My problem is to calculate $E(e^{\lambda X})$, where X has normal distribution $N(\mu, \sigma^2)$. So I have to calculate integral as follows: $\int_{-\in...