a. Let X, have a chi-squared distribution with parameter v, (see Section 4.4), and let X, be independent of X, and have a chi-squared distribution with parameter 2.

Use the technique of Example 5.21 to show that X + X, has a chi-squared distribution with parameter

b. In Exercise 71 of Chapter 4, you were asked to show that if Z is a standard normal rv, then Z2 has a chi-squared distribution with 1.

Let Z1, Z2, ..., Z, be n inde- pendent standard normal rv's. What is the distribution of Z++Z? Justify your answer.

c. Let X X be a random sample from a normal dis- tribution with mean and variance o. What is the dis- tribution of the sum Y = [(X)/]?? Justify your answer.