Consider a sequence ykk 1 of iid observations where under

Question

Question: Consider a sequence {Yk,k ≥ 1} of i.i.d. observations where under H0, the observations are uniformly distributed over [0, 1], so they admit the density

(a) Evaluate the generating function G0(u) of Zk = lnL(Yk).

(b) Use the expression for ln G0(u) obtained in (a) to evaluate the means m0 and m1 of Zk under H0 and H1, respectively.

(c) Obtain a closed form expression for the rate function 0(z) obtained by Legendre transformation of ln G0(u)

(d) Evaluate the Chernoff distance