Expectation of geometric distribution

• Distribution 2: Pr(0) = Pr(50) = Pr(100) = 1/3. Both have the same expectation: 50. But the first is much less “dispersed” than the second. We want a measure of dispersion. • One measure of dispersion is how far things are from the mean, on average. Given a random variable X , (X(s) − E(X)) measures how far the value of s is from the mean value (the expectation) of X . Define the variance of X to be Var(X) = E((X− E(X))) = Σs∈S Pr(s)(X(s)− E(X)) 2