Chun Li has derived an extension of Problem 10 for hidden multinomial trials. Let N denote the number of hidden trials, θi the probability of outcome i of k possible outcomes, and L(θ) the loglikelihood of the observed data Y . Derive the EM update

θn+1 i = θn i +

θn i

E(N | Y,θn)





∂

∂θi L(θn) −

k j=1

θn j

∂

∂θj L(θn)



 .

Here the superscripts indicate iteration number.