Compute Expected and Variance A computer user tries to reca

Compute Expected and Variance

. A computer user tries to recall her password. She knows it can he one of 4 possible pass words. She tries her passwords until she finds the right one. Let X he the number of wrong passwords she uses before she finds the right one. Find E(X) and Var(X).

Solution

X=0,1,2,3

E(x) = sigma xp and var(x) = sigma (x-mu)^2 p , where p is probability of x

E(X) = 0*(1/4) + 1*(3/4)(1/3)+2*(3/4)(2/3)(1/2)+3*(3/4)(2/3)(1/2) = 0+1/4+2/4+3/4 = 6/4 = 1.5

Var(X) = (0-1.5)^2 * (1/4) + (1-1.5)^2 * (1/4) + (2-1.5)^2 * (1/4) + (3-1.5)^2 * (1/4) = 5 * (1/4) = 5/4 = 1.25