Let a random experiment be the casting of a pair of fair dic

Let a random experiment be the casting of a pair of fair dice, each having six faces, and let the random variable X denote the sum of the dice.

(a) With reasonable assumptions, determine the pmf f (x) of X. Hint: Picture the sample space consisting of the 36 points (result on first die, result on second die), and assume that each has probability 1/36. Find the probability of each possible outcome of X, namely,x = 2, 3, 4, . . . , 12.

(b) Draw a probability histogram for f (x).

Solution

The following outcomes is coming for casting of a pair of fair dice

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

let the random variable X denote the sum of the dice.

the pmf f (x) of X

(b)