5. Suppose that the average number of accidents at an intersection is two per day.

(a) Use Markov’s inequality to find a bound for the probability that at least five accidents will occur tomorrow.

(b) Using Poisson random variables, calculate the probability that at least five accidents will occur tomorrow. Compare this value with the bound obtained in part (a).

(c) Let the variance of the number of accidents be two per day. Use Chebyshev’s inequality to find a bound on the probability that tomorrow at least five accidents will occur.