If the independent variables X 1 and X 2 have means 1 , 2 and variances 2 1 , 2 2 , respectively, show that the mean and variance of the product Y X 1 X 2 are 1 2 and 2 1 2 2 2 1 2 2 2 2 2 1 , respectively ...

Solution We have Y X1X2 EY EX1X2 EX1 ...

If the independent variables X 1 and X 2 have means 1 , 2 and

Question:

If the independent variables X₁ and X₂ have means μ₁, μ₂ and variances σ²₁, σ²₂, respectively, show that the mean and variance of the product Y = X₁X₂ are μ₁μ₂ and σ²₁σ²₂ + μ²₁σ²₂ + μ²₂σ²₁, respectively.