Unformatted text preview: e have:
Independent *Proof of #3
If we can show
Approach 1: p.d.f. Approach2: are independent then we have proven that m.g.f. Solution: The MGF approach (***make sure you know the MGF approach).
Recall: (1) The joint m.g.f. of X and Y is defined as:
Recall: (2) Recall: (3) X and Y are independent if and only if
Now back to our proof: 3 The above derivation also shows that and *Proof of #2 We have already proven in #3 above that
One can easily prove (using mgf for example), that its Z-score,
(using the 2nd Definition of Chi Square Distribution or recall our
proof from Lecture 6, review of the transformations.) Additional Questions and Solutions Q1. Prove
Solution for any distribution/population. 4 Q2. (1). Please point out a chi-square random variable with k degrees of freedom
corresponds to which particular gamma distribution. (2). Please write down the
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This document was uploaded on 03/15/2014 for the course AMS 412 at SUNY Stony Brook.
- Spring '14