# Question

Prove Theorem 8.9.

Theorem 8.9

If X1, X2, . . . , Xn are independent random variables having chi- square distributions with v1, v2, . . . , vn degrees of freedom, then

Has the chi-square distribution with v1 + v2 + · · · + vn degrees of freedom.

Theorem 8.9

If X1, X2, . . . , Xn are independent random variables having chi- square distributions with v1, v2, . . . , vn degrees of freedom, then

Has the chi-square distribution with v1 + v2 + · · · + vn degrees of freedom.

## Answer to relevant Questions

Prove Theorem 8.10. Theorem 8.10 If X1 and X2 are independent random variables, X1 has a chi-square distribution with v1 degrees of freedom, and X1 + X2 has a chi-square distribution with v > v1 degrees of freedom, then X2 ...Use the method of Exercise 8.25 to find the approximate value of the probability that a random variable having a chi-square distribution with v = 50 will take on a value greater than 68.0. Show that for v2 > 2 the mean of the F distribution is v2 / v2 – 2, making use of the definition of F in Theorem 8.14 and the fact that for a random variable V having the chi-square distribution with v2 degrees of freedom, ...Verify the results of Example 8.4, that is, the sampling distributions of Y1, Yn, and X~ shown there for random samples from an exponential population. With reference to part (b) of Exercise 8.52, find the covariance of Y1 and Yn.Post your question

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