1. A fair coin is tossed three times. A player wins $1 if the first toss is a head, but loses $1 if the first toss is a

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1 A Fair Coin Is Tossed Three Times A Player Wins 1 If The First Toss Is A Head But Loses 1 If The First Toss Is A 1 (83.74 KiB) Viewed 109 times

1. A fair coin is tossed three times. A player wins $1 if the first toss is a head, but loses $1 if the first toss is a tail. Similarly, the player wins $2 if the second toss is a head, but loses $2 if the second toss is a tail, and wins or loses $3 according to the result of the third toss. Let the random variable X be the total winnings after the three tosses (possibly a negative value if losses are incurred). a) Construct the probability mass function. b) Construct the cumulative distribution function. c) What is the variance of this random variable?