Suppose the number of parking tickets X issued police officer\'s shift has the p

Question

Suppose the number of parking tickets X issued police officer's shift has the probability distribution (a) Find the mean and standard deviation of the number of parking tickets issued. (b) Let A = [X lessthanorequalto 2] and B = [X greaterthanorequalto 1]. Find P(A | B) = P[X lessthanorequalto 2 | X greaterthanorequalto 1]. (c) Suppose the numbers of tickets issued on different days are independent. What is the probability that, over the next five days, no parking tickets will be issued on exactly one of the days?

Explanation / Answer

a) Mean, E(X) = 0 * 0.13 + 1 * 0.14 + 2 * 0.43 + 3 * 0.2 + 4 * 0.1

                       = 2

E(X2) = 02 * 0.13 + 12 * 0.14 + 22 * 0.43 + 32 * 0.2 + 42 * 0.1

          = 5.26

Var(X) = E(X2) - (E(X))2

           = 5.26 - 22

           = 1.26

Standard deviation = sqrt(1.26) = 1.12

b) P(B) = P(X > 1) = 1 - P(X = 0) = 1 - 0.13= 0.87

P(A and B) = P(1 < X < 2) = P(X = 1) + P(X = 2) = 0.14 + 0.43 = 0.57

P(A | B) = P(A and B) / P(B) = 0.57 / 0.87 = 0.66

c) P(X = 0), p = 0.13

n = 5

P(X = x) = 5Cx * 0.13x * (1 - 0.13)5-x

P(X = 1) = 5C1 * 0.131 * 0.874 = 0.3724

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