Let Y1 Y2 Y5 Be Independent Random Variables With Probability Distributions That

Please answer the following question related to G-test, likelihood ratio test

Let Y1, Y2, Y5), be independent random variables with probability distributions that areNormal(m, (:2 = 1). That is, 1 — % (1;;- —Hi, )2B f(yé|#é)=m i=11253 _OO<,U"E<+OO The null hypothesisis of homogeneity states that all 3 random variables have the same Normaldistribution, i.e., Ho : p1 = pig = M3 = a. The alternative hypothesis states that at least 2 ofthe m’s are different. (a) Please derive G2, — for testing the null hypothesis of homogeneityversus the alternative hypothesis. Simplify as much as possible. (RECALL: 221:1 K; = n?) (b) What is the large sample probability distribution for G2 in this problem?

 

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