A casino offers you the following game. There’s a pot that initially contains 1 dollar. A fair coin is tossed. If it comes up tails, the amount of money in the pot is doubled, and the coin is tossed again. The game ends once the coin comes up heads, at which point you get whatever is in the pot. Let the random variable X denote the amount of money you win by playing this game.

(a) What is the set X of possible values for X.

(b) Write down the PMF pX (x) of X for x ∈ X .

(c) What’s the probability that you’ll win less than 20 dollars?

 (d) Compute E[X].

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