Question

Now assume we do not know which coin is tossed in each experiment, and we decide to use the EM algorithm to estimate θA,θB . Suppose we initialize the parameters as θ0A=0.6 and θ0B=0.4 . Also, we initially think coin A and coin B are selected with equal probability and independently in each experiment.

Experiment | Coin | Outcome
1 | ? | H T T H
2 | ? | H H H T
Perform the first iteration of E-step, find the value of Q1(z(1)=A) , i.e. the conditional probability that coin A is selected in Experiment 1, and Q2(z(2)=A) , i.e. the conditional probability that coin A is selected in Experiment 2.

(Enter numerical answers accurate to at least 2 decimal places. )

Q1(z(1)=A)=
unanswered
Q2(z(2)=A)=
unanswered
After performing the first iteration of E-step, perform the first iteration of M-step, find θ1A,θ1B , the value of θ after the first iteration of the EM algorithm.

(Enter numerical answers accurate to at least 2 decimal places. )

θ1A=
unanswered
θ1B=