Questions 14 and 15 are related A traffic survey at an intersection was conducted over one hour in 5 different occasions. The number of vehicles recorded in each hour were 42, 46, 55, 60, and 38. It is assumed that the number of vehicles arriving at the intersection follows a Poisson distribution. Which one of the following expressions gives a good representation of the posterior distribution of the mean rate of vehicles (v) at the intersection assuming a non- informative prior? O 1. In(p(v|D)) = K +25 In(v) -241v O 2, In(p(v|D)) = K + 241In(v)-5v O 3. In(p(v|D)) = K + 241 In(v)-25v O 4. In(p(v| D)) = K +5In(v) - 241v QUESTION 15 Use the information from Question 14 and determine the posterior distribution of the mean rate of vehicles (v) arriving at the intersection per hour. To determine the posterior function of v, do your calculations between a mean rate of 30 and 70 vehicles per hour with steps of 0.1. Respond the following: 1. The mean value of the posterior is v = 2. The standard deviation of the posterior is 3. The norm of the posterior distribution of v is equal to Note: round your answers to only three decimals. Make sure you implement the trapezoid rule (see Computer Lab 04) to estimate the normalizing constant.