question_answer 1)

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X. 

Answer:

Since X denotes the sum of the numbers obtained when two fair disc are rolled.       Therefore X = 2, 3, 4, 5, 6, 76, 8, 9, 10, 11, 12       X = 2 = {1, 1}       X = 3 = {(1, 2), (2, 1)}       X = 4 = {(1, 3), (2, 2), (3, 1)}       X = 5 = {(1, 4), (2, 3), (3, 2), (4, 1)}       X = 6 = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}       X = 7 = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}       X = 8 = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}       X = 9 = {(3, 6), (4, 5), (5, 4), (6, 3)}       X = 10 = {(4, 6), (5, 5), (6, 4) }       X = 11 = {(5, 6), (6, 5)}       X = 12 = {(6, 6)}.                                               and P (X = 12)       We have       And        Var (X) = E(X2) ? [E(X)]2       = 54.833 ? 49 = 5.833       and       = 2.415