Question 8

Consider the independent random variables Y₁ ~ x²(3) for i=1,2,..., 20

1. Using moment generating functions, determine the moment generating function of W

20

W = Y₁ + Y₂ + ... Y20 = Yi

i=1

(Hint: Use the table below with the fact that the Moment Generating Function of a sum of independent random

variables is just the product of the moment generating functions.)

2. Determine what the distribution of W is using the provided table below. What is the mean and variance of W?

3. Approximate P(W> 79.08) using the central limit theorem.

4. Use the x² table from class to determine P(W> 79.08) exactly. How good would you say your approximation

from part (3) is?