please help with practice problem

7. Let X1, X2, ..., X15 be a random sample from a population with probability density function (pdf): A if x > 1 x6+1' f (x|0) = 0, otherwise (a) Find the pdfs of Y1 = 20 In X, (where In denotes the natural logarithm) and show that T = 20 _ _ In X; ~ X30 (the chi-square distribution with 30 degrees of freedom); (b) For testing Ho: 0 = 1 against Ha: 0 > 1, find uniformly lost powerful test of level a = 0.1. Find the maximum and minimum values of power, as 0 varies under Ha