Can someone please help me with the attached problem, I really don't know where to start with it. I'd really appreciate some pointers in the right direction.
Thanks.
note that has a chi-squared distribution of degrees of freedom since each term in the sum is a squared normal random variable and is independent of other random variables in the sum. Then show that . The RHS is a chi-squared random variable with one degree of freedom. Since df's add, this implies that is a chi-squared distribution with degrees of freedom provided that and are independent.