This thread contains the ideas you need to use: http://www.mathhelpforum.com/math-he...tml#post119542
This thread contains the ideas you need to use: http://www.mathhelpforum.com/math-he...tml#post119542
In fact, at second glance Q1 is even easier than I thought. The thread I referenced actually gives a solution to Q1 since
~ .
Q2:
The moment generating function of is:
(which by the way is recognised as the moment generating function for the chi-squared distribution with 1 degree of freedom).
Therefore the moment generating function of
(since are i.i.d. random variables).
This is recognised as the moment generating function for the chi-squared distribution with n degrees of freedom. And since when a moment generating function exists there is a unique distribution corresponding to that moment generating function, ....