Use the definition in Expression (3.13) to prove that V(aX + b) = σ2. σ2x [ Hint: With h...

Use the definition in Expression (3.13) to prove that V(aX + b) = σ². σ²_x [ Hint: With h(X) = aX + b, E[h(X)] = aµ = b where µ = E(X).]

Reference Expression (3.13

The variance of h(X) is the expected value of the squared difference between h(X) and its expected value:

When h(X) = aX + b, a linear function,

Substituting this into (3.13) gives a simple relationship between V[h(X)] and V(X):