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

Question

A fair coin is tossed three times. A player wins $1 if the first toss is a head, but loses Si 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). Construct the probability mass function. Find the expectation and the standard deviation of X.

Explanation / Answer

In this case the player can result one of the following outcomes:

(TTT, HHT, HTT, THH, THT, TTH, HTH, HHH)

The random variable X – Total winning of the bet possesses the values with respect to the above trails as : -6,-4,-2,0,2,4,6

X

-6

-4

-2

0

2

4

6

P(X)

1/8

1/8

1/8

2/8

1/8

1/8

1/8

X

-6

-4

-2

0

2

4

6

P(X)

1/8

1/8

1/8

2/8

1/8

1/8

1/8

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