Question: Please help me solve this question. Thanks a lot! 7. A positive random variable Y is said to be a lognormal random variable, LOGN(u, o?),

Please help me solve this question. Thanks a lot!

7. A positive random variable Y is said to be a lognormal random variable, LOGN(u, o?), if In Y ~~ N(u, o?). We assume that Y, ~ LOGN((, ?), i=1, ...,n are independent. [5] (a) Find the distribution of T = 1In Yi. [4] (b) Find E(T) and Var(T) 5] (c) If we assume that /1 = ... = An and of = ... = 0%, what does the the successive geometric average, lim (1IRY4)", converge in probability to? Justify your answer. [4] (d) If we assume that /1 = ... = and of = ... =02, i.e., Y's are i.i.d, find the maximum likelihood estimator of E(Y1)

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