Let the Mean and Variance of five observations x 1 = 1 , x 2 = 3 , x 3 = a , x 4 = 7 and x 5 = b , a b , be 5 and 10 respectively. Then the Variance of the observations n + x n , n = 1 ,

Question

Let the Mean and Variance of five observations x 1 ​ = 1 , x 2 ​ = 3 , x 3 ​ = a , x 4 ​ = 7 and x 5 ​ = b , a > b , be 5 and 10 respectively. Then the Variance of the observations n + x n ​ , n = 1 , 2 , …… ..5 is

TestHub · Accepted Answer

​ x ˉ = n ∑ x i ​ ​ = 5 1 + 3 + a + 7 + b ​ = 5 a + b = 14 σ 2 = n ∑ x i 2 ​ ​ − ( x ˉ ) 2 ⇒ 5 1 2 + 3 2 + a 2 + 7 2 + b 2 ​ − 25 = 10 a 2 + b 2 = 116 a > b a = 10 b = 4 n + x n ​ : 2 , 5 , 13 , 11 , 9 ​ ​ σ 2 = 5 2 2 + 5 2 + 1 3 2 + 1 1 2 + 9 2 ​ − ( 5 2 + 5 + 13 + 11 + 9 ​ ) 2 = 80 − 64 = 16 ​ option 4

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