The game of craps is played with two (fair) six-sided dice. On the first roll we are interested in the sum of the face-up values of the dice (the first roll can be considered a random variable, X). Possible values of the first roll have a range of 2-12 (seen in the first row of the following table). The probability of observing any one of these particular values on the first roll can be found in the second row.

 Value 2 3 4 5 6 7 8 9 10 11 12 

Probability 1 36 2 36 3 36 4 36 5 36 6 36 5 36 4 36 3 36 2 36 1 36

a) Draw the pdf associated with the value of the first roll (the random variable).

b) What is the expected value of the first roll (E(X))?

c) What is the probability of “crapping out” (rolling a 2, 3 or 12 on first roll)?

D) Draw the cdf associated with the first roll in craps (X). Using the cdf, calculate F(X ≤ 10).