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A fair die is thrown. If the number on the die is 2 or less, a...

A fair die is thrown. If the number on the die is 2 or less, a random variable X is assigned the value 1 and the value zero otherwise. The random variable X is then input to a binary channel with crossover probabilities v = 0.001 and e = 0.003. The output of the binary channel is the random variable Y. Find the following:

(a) Pr[ '3' | X = 0] or the probability that the die throw is 3 given that the random variable X is zero.

(b) Pr[X = 0|Y = 0] or the probability that X = 0 given that we observe Y = 0.

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