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1.Suppose you start with eight pennies and flip one fair coin. If the coin comes up

heads, you get to keep all your pennies; if the coin comes up tails, you have to give

half of them back. Let X be the total number of pennies you have at the end. Compute

E(X)

how do you find E(X)???

2. Suppose you roll one fair six-sided die and then flip as many coins as the number

showing on the die. (For example, if the die shows 4, then you flip four coins.) Let

Y be the number of heads obtained. Compute E(Y)