6.5.6. Suppose a sufficient statistic exists for the parameter 8. Use Thecrem 5.6.1 to show that the critical region of a likelihood ratio test wil l depend on the sufficient statistic.
7.l.1. Show directly-without av1.,,uu to the fact th.at x is .a gamma r-andom variable-that
f y( y ) as :stated in a true probability den&ity function_
7.3.2. Fmd the function for .a chi square random variable and use it to show that E(x ;) = n Var(x) = 2.n.
7.U ls it that the numbers 65, 30, and 55 are a random sample of size- 3 from a norma l distribution with µ 50 and u = 10? Answer the question byusing a chi square
distribution. Hinr.: = (Yi - 50)/10 and use Theorem 7.3.1.
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