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I roll a six-sided die and observe the number N on the uppermost face. I then toss a fair coin N…

I roll a six-sided die and observe the number N on the uppermost face. I then toss a fair coin N times and observe X, the total number of heads to appear. What is the probability that N = 3 and X = 2? What is the probability that X = 5? What is E[X], the expected number of heads to appear?

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