Homework 1

Homework 1 is due 9/6/2022 at 11:59 PM. Submit your homework on Canvas as one PDF document.

The PDF version of this assignment can be found here.

1. $X\sim Bin(n,p)$, show the variance of Binomial distribution to be $np(1-p)$.
2. $X\sim Pois(\lambda)$ , show the variance of a Poisson distribution to be $\lambda$.
3. $X\sim Unif(a,b)$, show the variance is a $\frac{(b-a)^2}{12}$.
4. $X\sim N(\mu,\sigma^2)$, show the variance to be $\sigma²$.
5. Prove one of the following:

   1. $X\sim Gamma(\alpha,\beta)$, find the $E(X)$.

   2. $X\sim Beta(\alpha,\beta)$, find the $E(X)$

6. Find a distribution where the expected value does not exist.