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.

flashcards

QuestionAnswer
What is the relationship between the expected values of Y and X when Y = aX + b?E(Y) = aE(X) + b
What is the relationship between the variance of Y and the variance of X when Y = aX + b?Var(Y) = a^2 Var(X)
Given a discrete random variable Y = aX + b, what is the formula to find E(Y) if E(X) is known?E(Y) = aE(X) + b
Given a discrete random variable Y = aX + b, what is the formula to find Var(Y) if Var(X) is known?Var(Y) = a^2 Var(X)