Question: Let Y1,Y2,...,Yn be independent and identically distributed random variables from a Gamma distribution with shape parameter and scale parameter . Given the scenarios below, determine

Let Y1,Y2,...,Yn be independent and identically distributed random variables from a Gamma distribution with shape parameter and scale parameter . Given the scenarios below, determine whether you would be able to find a uniformly most powerful rejection region for the hypothesis test. Explain your answer in each case.

(a) H0 : = 0 and Ha : > 0 with known.

(b) H0 : = 0 and Ha : < 0 with unknown.

(d) H0 : = 0 and Ha : > 0 with unknown.

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