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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