3. Suppose that a trucking company owns a large eet of wellmaintained trucks and assume that breakdowns appear to occur at random times and follow Poisson distribution. The president of the company is interested in learning about the current daily rate (3.}at which breakdowns occur. Assume daily breaks are independent. (a) Assume the president observed the breakdowns in n consecutive days (x1, x2, ....,X,). Derive the Maximum likelihood estimate of 2.. (b) Using your answer from part (a), determine the probability that at most 8 orders are placed in a 1- minute interval. (c) Determine the probability that no orders are placed in the next 12 seconds. (d) What is the expected value and variance for the number of orders arriving in the next 12 seconds