Chapter 1 - Discrete Random Variables

The expected value of the discrete random variable X denoted E(X)

E(X) = ∑ xP(X = x)

The expected value of X²

E(X²) = ∑ x²P(X = x)

The computational formula for the variance of X

Var(X) = E(X²) - (E(X))²

The expected value of a function g(X)

E(g(X)) = ∑ g(x)P(X = x)

The expected value of the linear transformation aX + b

E(aX + b) = aE(X) + b

The expected value of the sum of two random variables X and Y

E(X + Y) = E(X) + E(Y)

The variance of the linear transformation aX + b

Var(aX + b) = a²Var(X)