Determining the den-sity function

Question

Assignment:

Suppose Y₁, Y₂, Y₃, and Y₄ are independent random variables, each with den-sity function

f_θ(Y) = θe^-θy, for y > 0,

where θ > 0 is an unknown parameter. Interest is in testing H_o θ = 2 versus H_a : θ = 4. Find the decision rule for the most powerful test of size α = .05. State the decision rule by filling in the blanks and circling either "greater" or "less" as appropriate:

Reject H_o when_{-------------}  is (greater or less) than c, where c is the_----------- th quantile of a_{---------------} distribution.