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Now assume we do not know which coin is tossed in each experiment, and we decide...

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)=

Q2(z(2)=A)=

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=

θ1B=

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