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The Mongol general Subudai is expecting reinforcements from Chenggis Kahn before attacking King Bela of Hungary. The probability mass function describing the number N of tumens (units of 10,000 men) that he will receive is

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If he receives N = k tumens, then his probability of losing the battle will be 2-k. This can be described by defining the random variable W which will be 1 if the battle is won, 0 if the battle is lost, and defining the conditional probability mass function

1918_3ff7e391-0616-401e-8819-3bcd6beaf4e4.png

(a) Find c.

(b) Find the (unconditional) pmf pW(m), that is, what is the probability that Subudai will win or lose?

(c) Suppose that Subudai is informed that definitely N

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