Let X n = {X 1,. ... ... , X n} ∼ Uniform (θ, θ + 1). It is necessary to test the hypothesis H 0: θ = 0 vs. H 1: θ> 0. In this case, the Wald test cannot be used, since the estimates of θ do not converge to the normal as n → ∞ distribution. We will use the following rule: the hypothesis H 0 is rejected if X (n) ≥ 1 or X (1) ≥ c, where c is some constant, X (1) = min {X 1,. ... ... , X n}, X (n) = max {X 1,. ... ... , X n}. (a) Find the power function for the given test. (b) At what value of parameter c will the test size be equal to 0.05? (c) Find n ≥ 1 such that for θ = 0.1 and test size 0.05, the test power is not less than 0.8.