[b] The carparic in front of a small shop comprises 3 parking spaces The number of cars (i.e. occupied spaces) is recorded every 10 minutes. starting at [17:00 (opening time} when the number is zero. Using these data, the probability that the number of cars changes after 10 minutes is estimated to be three times the probability that the number does not change. Any change is at most i1, and equiprobable where there is a choice. The only exception to these dynamics is when the carpark is full. Then. the number of cars after 10 minutes is 3. 2 or 1, with probabilities 0.5. 0.3 and 0.1. respectively. Note: these dyanamics imply that the long-run [i.e. stationary) probabilities are 0.2. 0.3. 0.3 and 0.2 (for l], II 2 and 3 cars, respectively). (i) Specify the computations needed to process 14 hours of these data into sufcient statistics for estimating T. the transition matrix of a HMC model of the sequence. Provide an example of these statistics, consistent with the estimated dynamics above. [25 %] [ii] lfthe carpark first fills up at 07:40. what is the probability that there was one car at 07:20? [29 %] (iii) lfthe carpark is full at 19:00. what is the probability that it was not full 20 minutes eariier? [15 x]