Solution-Find the critical region for a test that is

Suppose we observe a random variable X having the exponential distribution with parameter A, which means that X has pdf

fX(x;λ) = {λe^-λxif x ≥0

{0 otherwise

(a) Find the critical region for a test that is uniformly mast powerful for testing Ho: λ= 4 against H1 : λ > 4 at level of significance .05.

(b) Find the critical region for a test that is uniformly most powerful for testing Ho : λ = 4 against H1 : λ < 4 at level of significance .05.

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