Question

1.) Consider two independent discrete random variables X and Y with V(X)=2 and V(Y)=5. Find V(4X-8Y-9).

2.) Consider two independent discrete random variables X and Y with SD(X)=16 and SD(Y)=9. Find SD(5X-2Y-13). (Round your answer to 1 place after the decimal point).

3.)Consider two discrete random variables X and Y with V(X)=81 and V(Y)=36 and correlation ρ=0.7. Find V(X-Y). (Round your answer to 1 digit after the decimal point).

Answer 1

1)

Var ( 4 X - 8Y - 9) = 4² Var(X) + 8² var(Y) - 8 * 4 * 2 Cov (X, Y)

= 16 * 2 + 64 * 5 + 0 (For independent variables , Cov ( X , Y) = 0 )

= 352

2)

Var ( 5X - 2Y - 13) = 5² Var(X) + 2² var(Y) - 5 * 2 * 2 Cov (X, Y)

= 25 * 16² + 4 * 9² + 0 (For independent variables , Cov ( X , Y) = 0 )

= 6724

SD ( 5X - 2Y - 13) = sqrt { Var { 5X - 2Y - 13 } }

= sqrt { 6724)

= 82

3)

= Cov (X , Y) / sqrt ( Var (X) * Var(Y) )

Cov (X , Y) = * sqrt ( Var (X) * Var(Y) )

= 0.7 * sqrt ( 81 * 36)

= 37.8

Var ( X - Y) = Var(X) + Var (Y) - 2 Cov (X , Y)

= 81 + 36 - 2 * 37.8

= 41.4