In a probability exam, X is a random variable and Y = 4X + 1 is another random variable. The probabilities for X are given as P(X=1) = 1/2, P(X=2) = 1/4, and P(X=4) = 1/4. The expected value of X is 2, the expected value of X² is 5.5, and the variance of X is 1.5. The expected value of Y is 9 and the variance of Y is 24. Using linearity of expectation, we can find that E(X + Y) = E(X) + E(Y) = 11. Now, we need to find var(X + Y), which is equal to var(X + 4X + 1) = var(5X + 1). Can anyone explain why var(5X + 1) = 25var(X)?