a. Let X1 have a chi-squared distribution with parameter n1 (see Section 4.4), and let X2 be independent of X1 and have a chi-squared distribution with parameter v2. Use the technique of Example 5.22 to show that X1 + X2 has a chi-squared distribution with parameter v1 + v2.
b. In Exercise 71 of Chapter 4, you were asked to show that if Z is a standard normal rv, then Z2 has a chisquared distribution with n = 1. Let Z1, Z2, . . . , Zn be n independent standard normal rv's. What is the distribution of Z21 + ...+ Zn2? Justify your answer.
c. Let X1, . . . , Xn be a random sample from a normal distribution with mean m and variance s2. What is the distribution of the sum Y = Σni-1[(Xi - µ)/σ]2? Justify your answer.