Homework 5

Assignment is due April 6, 2023 @ 11:59 PM

March 31, 2023

Problem 1

X\sim Pois(\lambda), what is the moment generating function of Y=3X+4

Problem 2

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.

Problem 3

Let X_1, \ldots, X_n\overset{iid}{\sim}Beta(\alpha,\beta). What is the expected value and variance of Y_n=\sum^n_{i=1}X_i

Problem 4

Let X_1, \ldots, X_n be iid with E(X)=e^\theta and Var(X)=e^{\theta²}. What is the distribution of \bar X if n\rightarrow \infty?