The mean of five numbers is 0 and their variance is 2 . If three of those numbers are - 1 , 1 and 2 , then the other two numbers are

Step-by-step solution

Let the other two numbers be x and y . According to the question, Mean = - 1 + 1 + 2 + x + y 5 = 0 ⇒ x + y = - 2 … i Also, σ 2 = 2 ⇒ - 1 - 0 2 + 1 - 0 2 + 2 - 0 2 + x - 0 2 + y - 0 2 5 = 2 ⇒ 1 + 1 + 4 + x 2 + y 2 = 10 ⇒ x 2 + y 2 = 4 … i i ⇒ x + y 2 - 2 x y = 4 ⇒ 4 - 2 x y = 4 ⇒ x y = 0 … i i i Now, x - y 2 = x 2 + y 2 - 2 x y = 4 - 0 = 4 using i i and i i i … i v ⇒ x - y = ± 2 Solving i and i v , we get, If x - y = 2 , x = 0 , y = -