Homework 1

Published

August 29, 2022

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.