Question: Consider the observation model YK = 01/2SK RK + Nk, k = 1,2,...,n where $1, 82, . .., s, is a known signal, N1, N2,

Consider the observation model YK = 01/2SK RK + Nk, k = 1,2,...,n where $1, 82, . .., s, is a known signal, N1, N2, ..., Nn, R1, R2. . .. . R. are i.i.d. /(0, 1) random variables, and 0 2 0 is an unknown param- eter. (a) Find the likelihood equation for estimating 0 from Y1, Y2, ..., Yn. (b) Find the Cramer-Rao lower bound on the variance of unbiased estimates of 9. (c) Suppose $1, $2, . .., $, is a sequence of +1's and -1's. Find the MLE of 6 explicitly. (d) Compute the bias and variance of your estimate from (c), and compare the latter with the Cramer-Rao lower bound

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