Could you please assist me in solving part (b) in the following question (screenshot)?

The universal data compression deals with describing nlength data sequence as from the source alphabets X", when the source distribution P is unknownl. Now, consider that the source distributions P are, instead of being completely unknown, restricted to a class of parametric distributions M = {Pam :9 e 9} which have corresponding codelengths log(P(93|6))2. Note that m is the data to be compressed, and the collection of data compressors is indexed by 9. Let 0 2 0(99) be the maximum likelihood estimate of the parameter 0 after observing as, i.e., P(x|) = mgxP(a:|6) However, this is not available to us, and without a prior knowledge of 63(35), we do not know how to decode, since we do not know the code design (without knowledge of the distribution to which the encoder is designed). Therefore, we code the data using an arbitrary distribution Q($). For example, a possible choice of Q($) could be an empirical distribution after observing m. In this part of the project, we will nd the optimal Q(r). (a) Explain mathematically and in words, what does the following term represent? P($I9) log 1 (QM () (b) The worst case value of (1) over individual sequences $ is max 0 P($|) I 1g( cm) ) And we want to minimize the worst case value with an optimal choice of the distribution was), A . P($|6) ngnmfixlog ( QM) ) (2) Then show that Qm_P@m C = Z P($I9($)) 5062'? is the optimal solution to (2). Q" is also known as the normalized maximum likelihood