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Let xb a random variable a and b are constants, Var(y) = (σ_y) ^2 = Var...

Let xb a random variable a and b are constants, Var(y) = (σ_y) ^2 = Var (a+bx) = Var(a) + Var (bx) = 0 + b^2 Var (x) = b^2 (σ_x) ^2 . prove that.

and prove:

1) y = a - bx

Var(y) = Var(a-bx) = b^2  (σ_x) ^2

2) z = x+y x and y are independent

Var(z) = Var(x+y) = Var(x) +Var(y) = (σ_x) ^2 + (σ_y) ^2

3) z = x-y

Var(z) = (σ_x) ^2 + (σ_y) ^2

Math   Statistics-And-Probability   
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