answer all 4 questions with explanation

Q.6 The numbers of cars, N. = k.. i = 1,2. ...,, passing a particular point on a rural road are recorded during n non-overlapping time-intervals, each of duration 5 minutes, as displayed in Table Q.6 for n =14. In an effort to study the influence of local roadworks on these numbers, the data also record whether these roadworks are active (A, = 1) or not (A, = 0) during each interval. N 13 15 11 15 31 27 17 17 20 30 26 22 22 16 0 0 1 10 0 0 1 0 Table Q.6 Process these data into appropriate parametric models for prediction of future counts and arrival times of cars, stating your assumptions. Hence, address each of the following: (a) Let 73) (s) be the time to arrival of the 3rd-next car. Evaluate the probability that 7(3) > 16 s. [25 %] (b) Evaluate the mean and standard deviation of 7 (s), being the time to arrival of the third-next car [25 %] (c) If a future sequence of measurements of the times. 7, 1 2 3 , between consecutive cars is collected. what is the probability that the first outlier time - Le. one that falls outside the standard interval of 1 - occurs for jc (25 %] (d) if a future count of cars in a 5-minute interval is 20. deduce and plot the probability density function of ! (s), being the time to arrival of the first car in this interval