Discrete Random Variables

binomial and uniform distributions are discrete random variables; geometric and poisson are infinite discrete random variables

When you compare two probability distributions, it is reasonable to calculate a measure of spread(variance or standard deviation) and central tendency (mean or expectation)

Expectation = sum of (r * probability of X=r)

then variance can be calculated by using E(X²) - E(X)²

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

E(cX) = cE(X)

E(d)=d

Var(X) only differs when the number infront of X changes, then Var(X) times the number², Var(d)=0 - a constant does not have any variations

This rule is the same as the one applies to mean and standard deviation

E(X1+X2) = E(X1)+E(X2), E(X1-X2) = E(X1)-E(X2)

Var(X1+X2) = Var(X1)+Var(X2), Var(X1-X2) = Var(X1)+Var(X2),