For the set A= x₁, x₂, x₃, x₄, x₅ the variance is 4 and the mean is 2 . For the set B=0 y₁, y₂, y₃, y₄, y₅ the variance is 5 and the mean is 4 . Then, the variance of A B is

Step-by-step solution

aligned & (c) A= x₁, x₂, x₃, x₄, x₅ & Mean = x_i 5 =2 _ i=1 ^5 x_i=10 & Variance, 1 5-1 [ x_i^2- ( x_i )^2 5 ]=4 & = 1 4 [ x_i^2- (10)^2 5 ]=4 & & x_i^2-20=16 & B= y₁, y₂, y₃ y₄, y₅ , Mean = _ i=1 ^5 y_i 5 =4 aligned y_i=20 Variance, 1 5-1 [ y_i^2- ( y_i )^2 5 ]=5 array rrr & 1 4 [ y_i^2- (20)^2 5 ]=5 & y_i^2-80=20 & y_i^2=100 array Now, A B= y₁, y₂, , y₅, x₁, x₂, . , .x₅ = a_i ; i=1,2, 10 aligned Variance & = 1 10-1 [ a_i^2- ( a_i )^2 10 ] & = 1 9 [ (x₁^2+x₂^2+ +x₅^2+y₁^2+ y₅^2 ) . & .- 1 10 x₁+ +x₅+y₁+ +y₅ ^2 ] &