Consider a random sample Y, ..., Yn from the mixture distribution with density f(y) = p.fLogNormal (y; , o) + (1 - p) fExp(y; ), with 1 UV 2? fExp(y; ) = A exp{-\y}, fLogNormal (y; , ): exp - )}, 1 {-2/2 (logy-1 20 y 0, X>0, y> 0, ER, > 0, and 0 = (p, , o, X). (a) (13 marks) Derive the EM algorithm to find the updating equations for (t+1) = (p(t+1), (t+1), (o(t+1)), X(t+1)).