If a and b are constants, then E(aX + b) = aE(X) + b.
E(aX) = aE(X)
E(b) = b
…Expected value of a constant is always a constant
For random variables X and Y , E(X + Y ) = E(X) + E(Y ).
Also, E(aX + bY ) = aE(X) + bE(Y ). ….basically take the constants out
Variance when X is Discreet
Variance when X is Random
….basically Variance of a Constant it zero
Bernoulli’s Distribution
E(X) = p
Var(X) = p(1-p)
Var (X) = p(1 - p)
Binomial Distribution (n independent trials )
X _ Binomial (n; p)
Bernoulli distribution is a special case of the binomial distribution with n = 1
If X _ Binomial (n; p), then
E(X) = np