a. A fair coin is flipped until the first tail appears. The player wins $2 if it occurs on the first flip, $4 if on the second flip, $8 if on the third flip and, in general, $2k if it occurs on the kth toss. Let X be a random variable that denotes the player's winnings. What is the pdf of X? Show that it satisfies the conditions required to be a proper pdf. What is the value of expected winnings? If the price to play this game was $10,000, would you play? Explain