Question: 14.11.3 Suppose that we take a random sample of size n from a normal distribution N(p, a'). We divide the observations into k groups of

14.11.3 Suppose that we take a random sample of size n from a normal distribution N(p, a'). We divide the observations into k groups of sizes n1, . . . , n k , where ni 2 2 for i = 1, . . . , k and n1 + ' . + nk = n. Let S; be the sample variance in the ith group. Find: (i) The distributionof [(nl - 1)s: + . . + (12k - l)S,]/a2. (ii) The distribution of S,"/Sl.

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