Unformatted text preview: e have:
Independent *Proof of #3
If we can show
and
and
are independent.
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 Zscore,
(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 chisquare random variable with k degrees of freedom
corresponds to which particular gamma distribution. (2). Please write down the
pdf, mgf,...
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This document was uploaded on 03/15/2014 for the course AMS 412 at SUNY Stony Brook.
 Spring '14

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