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

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Let Y1,Y2,.,Yn be independent and
identically distributed random variables
from a Gamma distribution with shape
parameter a and scale parameter B. 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) HO : B = B0 and Ha : B > B0 with a
known.
(b) HO : a = aO and Ha : a < a0 with B
unknown.
(c) HO : a = aO and Ha : a != a0 with B
known.
(d) HO : B = BO and Ha : B > B0 with a
unknown.
Transcribed Image Text:Let Y1,Y2,.,Yn be independent and identically distributed random variables from a Gamma distribution with shape parameter a and scale parameter B. 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) HO : B = B0 and Ha : B > B0 with a known. (b) HO : a = aO and Ha : a < a0 with B unknown. (c) HO : a = aO and Ha : a != a0 with B known. (d) HO : B = BO and Ha : B > B0 with a unknown.
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