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,...

a With But the inner integral can be shown to be equal to f ...

a. Let X1 have a chi-squared distribution with parameter n1 (see Section 4.4), and let X2 be

Question:

a. Let X1 have a chi-squared with parameter n1 (see Section 4.4), and let X2 be independent of X1 and have a chi-squared with parameter v2. Use the technique of Example 5.22 to show that X1 + X2 has a chi-squared 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 with n = 1. Let Z1, Z2, . . . , Zn be n independent standard normal rv's. What is the of Z21 + ...+ Zn2? Justify your answer.
c. Let X1, . . . , Xn be a random sample from a normal with mean m and variance s2. What is the of the sum Y = Σni-1[(Xi - µ)/σ]2? Justify your answer.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...