# Overview

This page will be populated in preparation for Finals week (mid-December 2020). In the meantime, use the Prob 140 textbook as an excellent resource in probability theory.

Here is a running list of topics that are currently covered:

• Counting provides us an intuitive method of figuring out how many possible ways there are to do something.

• More TBA!

## Reference

 Distribution Values Density Expectation Variance Links Uniform(m,n) [m, n] ​$\frac{1}{n-m+1}$​ ​$\frac{m+n}{2}$​ ​$\frac{(n-m+1)^2-1}{12}$​ ​ Bernoulli(p)Indicator 0, 1 P(X=1) = pP(X=0) = 1-p ​$p$​ ​$p(1-p)$​ ​ Binomial(n,p) [0, n] ​$\binom{n}{k}p^kq^{n-k}$​ ​$np$​ ​$np(1-p)$​ ​ Poisson($\mu$) ​$x\ge0$​ ​$e^{-\mu}\frac{\mu^k}{k!}$​ ​$\mu$​ ​$\mu$​ ​ Geometric(p) ​$x \ge 1$​ ​$(1-p)^kp$​ ​$\frac{1}{p}$​ ​$\frac{1-p}{p^2}$​ ​ Hypergeom.(N,G,n) [0, n] ​$\frac{\binom{G}{g}\binom{B}{b}}{\binom{N}{n}}$​ ​$n\frac{G}{N}$​ ​$n\frac{G}{N}\frac{B}{N}\frac{N-n}{N-1}$​ ​ Uniform Continuous (a, b) ​$\frac{1}{b-a}$​ ​$\frac{a+b}{2}$​ ​$\frac{(b-a)^2}{12}$​ ​ Beta(r,s) (0, 1) ​$\frac{\Gamma(r+s)}{\Gamma(r)\Gamma(s)}x^{r-1}(1-x)^{s-1}$​ ​$\frac{r}{r+s}$​ ​$\frac{rs}{(r+s)^2(r+s)}$​ ​ Exponential($\lambda$)(Gamma(1, $\lambda$)) ​$x\ge0$​ ​$\lambda e^{-\lambda x}$​ ​$\frac{1}{\lambda}$​ ​$\frac{1}{\lambda^2}$​ ​ Gamma(r, $\lambda$) ​$x\ge0$​ ​$\frac{\lambda^r}{\Gamma(r)}x^{r-1}e^{\lambda x}$​ ​$\frac{r}{\lambda}$​ ​$\frac{r}{\lambda^2}$​ ​ Normal(0,1) ​$x \in \mathbb{R}$​ ​$\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2}$​ 0 1 ​

Where $\binom{n}{k} = \frac{n!}{k!(n-k)!}$and $\Gamma(r) = \int_0^\infty x^{r-1}e^{-x}dx = (r-1)\Gamma(r-1) = (r-1)!$