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Let X1 , X2 , • • • , Xn and Yi, Y2 , • • • , Ym be independent random samples from the two normal distributions N( O, 81 ) and N(O, 82).

(a) Find the likelihood ratio l for testing the composite hypothesis H0 : 61 = 62 against the composite alternative H1 : 61 -::;: 62 •

(b) This A. is a function of what F-statistic that would actually be used in this test?

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