Question: Let X1, ., Xn and Y1, .., Y, be random and i.i.d samples respectively of size n with densities Beta (u, 1) and Beta(0, 1)

Let X1, ., Xn and Y1, .., Y, be random and i.i.d samples respectively of size n with densities Beta (u, 1) and Beta(0, 1) respectively. Also, let X and Y be independent of each other. Assume the testing of the following: Hotu=0 vs H : u+0 Note: the density of X ~ Beta(a, B) is f(x; a, P) = B(am) 1 x -1(1 - x)8-1, where: B(a,B) = [ ta-1(1 - t)3-1 is the Beta function, a, B > 0 and 0

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