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Roll a fair die, and let N be the number on the die. Then toss N times a biased coin (with probability 1/4 of tossing

Roll a fair die, and let N be the number on the die. Then toss N times a biased coin

(with probability 1/4 of tossing a head each time), and let H be the number of heads

in the N tosses.

a) Find the density functon of H.

b) Find E(H|N).

c) Find E(H).

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