Let the Mean and Variance of five observations x₁=1, x₂=3, x₃=a, x₄=7 and x₅=b, a b , be 5 and 10 respectively. Then the Variance of the observations n+x_n, n=1,2, . .5 is

Step-by-step solution

aligned & x = x_i n = 1+3+a+7+b 5 =5 & a+b=14 & ^2= x_i^2 n -( x )^2 & 1^2+3^2+a^2+7^2+b^2 5 -25=10 & a^2+b^2=116 & a b a=10 b=4 & n+x_n: 2,5,13,11,9 aligned aligned & ^2= 2^2+5^2+13^2+11^2+9^2 5 - ( 2+5+13+11+9 5 )^2 & =80-64=16 aligned option 4