Question

Let X and Y be two random independent variables with μ_X= 120, σ_X = 23, μ_Y = 370 and σ_Y = 21, find:

1. E(2 X− 1 Y + 290) =

2. Var(2 X− 1 Y + 290) =

3. SD(2 X− 1 Y + 290) =

Answer 1

1)

E( 2 X - 1 Y + 290 ) = 2 E(X) - E(Y) + 290

= 2 * 120 - 370 + 290

= 160

b)

Var( a X - bY) = a² Var(X) + b² Var(Y) - 2 * a * b Cov (X , Y)

So,

Var ( 2 X - 1 Y + 290 ) = 2² Var(X) + 1² Var(Y) - 2 * 2 * 1 Cov ( X , Y)

For independent variable, Cov ( X , Y) = 0

= 4 * 23² + 1 * 21² + 0

= 2557

c)

SD ( 2 X - 1 Y + 290 ) = sqrt [ Var ( 2 X - 1 Y + 290 ) ]

= sqrt [ 2557 ]

= 50.5668