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

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 the three tosses (possibly a negative value if losses are incurred).
(a) Construct the probability mass function.
(b) Construct the cumulative function.
(c) What is the most likely value of the random variable X?
Distribution
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