Transforming discrete random probabilities

Let’s say we have a discrete random variable, called X, and we know that there is another DRV which we can write as Y=aX+b - where a and b are constants.

If we know the expected value for X, as well as its variance, then we can also find the expected value and variance of Y!

Finding E(X)

E(Y)=aE(X)+b

See discrete random expectation transformation for an explanation.

Finding Var(X)

Var(Y)=a^2Var(X)

See discrete random variance transformation for an explanation.