Discrete random expectation transformation

For a discrete random variable, called X, if we know that there is another DRV which we can write as Y=aX+b - where a and b are constants:

E(Y)=a\,E(X)+b

Explanation

• If we add b to the result of any outcome of the DRV, we would expect to get, on average, a value b more than before (because we’ve shifted our entire distribution by b).
• When multiplying by a, we multiply the random variable X by a, so the average we can expect to get from X (so E(X)) is a times what it was.