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Probability Distribution, Expected value and Variance

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A player rolls two dice. The player receives $1 for each dot on the face of two dice. For example, he will be paid $9 if the face of the dice show a 4 and a five. let X= the number of dollars won each game.
a) is X a discrete or continuous random variable?
b) Show the probability distribution of X.
c) Find the expected value of X
d) Find the Variance of the payoff.

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(a) X is a discrete random variable
(b) Probability distribution of X:
X 1 2 3 4 5 6
P(X) 0/36 = 0 1/36 2/36 = 1/18 3/36 = 1/12 4/36 = 1/9 5/36 ...

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