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 three tosses (possibly a negative value if losses are incurred).

(a) construct the probability mass function

Question

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 three tosses (possibly a negative value if losses are incurred).

 (a) construct the probability mass function