Homework 3

Published

September 16, 2022

Homework 3 is due 9/23/2022 at 11:59 PM. Submit your homework on Canvas as one PDF document.

The PDF version of this assignment can be found here.

  1. Let X_1, X_2, \ldots, X_n\overset{iid}{\sim}N(\mu,\sigma^2) and Z_i = \frac{X_i-\mu}{\sigma}. Find the distribution of Y=\sum^n_{i=1}Z_i^2.

  2. Let X_1, X_2, \ldots, X_n\overset{iid}{\sim}N(\mu,\sigma^2) and a_1,a_2, \ldots,a_n be a set of known constants. Find the distribution of Y=\sum^n_{i=1} a_iX_i.

  3. Let X_1\sim Bin(n_1,p) and X_2\sim Bin(n_2, p). Find the distribution function of Y=X_1 + X_2. Assume X_1\perp X_2.