Question

(a) When the two dice are rolled, find the value of X for the 36 possible outcomes (i, j), where i and j are the numbers that appear on the first die and the second die, respectively. Assuming the random variable X is the sum of numbers that appear when a pair of dice is rolled.                                                                                                                                                                         

Answer 1

Given than two dice are rolled. And we need to find values of random variable X which is the sum of number that appear when pair of dice is rolled.

We have total of 36 possible outcome of (i,j), where i and j are the numbers that appear on the first die and the second die, respectively as given.

First, the possible values of i are (1, 2, 3, 4, 5, 6) and respectively of j also. So, the possible pairs of (i, j) and the Value of X are as follows:

(1,1) = 2, (1,2) = 3, (1,3) = 4, (1,4) = 5, (1,5) = 6, (1, 6) = 7,

(2,1) = 3, (2,2) = 4, (2,3) = 5, (2,4) = 6, (2,5) = 7, (2, 6) = 8,

(3,1) = 4, (3,2) = 5, (3,3) = 6, (3,4) = 7, (3,5) = 8, (3, 6) = 9,

(4,1) = 5, (4,2) = 6, (4,3) = 7, (4,4) = 8, (4,5) = 9, (4, 6) = 10,

(5,1) = 6, (5,2) = 7, (5,3) = 8, (5,4) = 9, (5,5) = 10, (5, 6) = 11,

(6,1) = 7, (6,2) = 8, (6,3) = 9, (6,4) = 10, (6,5) = 11, (6, 6) = 12.

So, the random variable X can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Hoping that the answer helps. Please comment for further assistance.