Suppose that buses arriving at a certain stop can be modeled as a Poisson process with a rate parameter of 6 per hour. (Give answers with 3 digits after decimal) a) [1pt] What is the probability that 5 buses arrive during an hour? Submit Answer. Tries 0/99 b) [2pts] What is the probability that no bus arrives during 40 mins? Submit Amver Tries 0/99 c) [2pts] Suppose you just arrive at this stop, what is the probability that you need to wait at least 25 minutes for the bus? Submit Apoem Tries 0/99 d) [2pts] What is the 40'th percentile of your waiting time (In hours]? Subma Arwer Tries 0/99 e) [1pt] What is your expected waiting time (in hours) ? Submit Answer Tries 0/99In a single channel automatic car wash, cars arrive following Poisson distribution at the rate of 20 per hour. It takes an average of 2 minutes to wash a car, and the service time follows exponential distribution. Find the following operating characteristics of the system (10 marks). a) What is the probability that 4 cars arrive within 10 minutes? b) What is the probability that no car arrives within 5 minutes? c) What is the probability that a car is washed in less than 1.5 minutes.(1 mark each) For each of the given matrices, select all decompositions that can be applied to it. You do not have to show your work for this question. 2 ) A = [61 O Diagonalization (i.e., A = PDP-1 with D diagonal) O Schur triangularization O Spectral decomposition O Singular value decomposition b ) B = 0 1.001 Diagonalization O Schur triangularization O Spectral decomposition Singular value decomposition c) C is the 75 x 75 matrix with every entry equal to 1. Diagonalization Schur triangularization O Spectral decomposition Singular value decomposition d) D = 0 1 1 Diagonalization OSchur triangularization Spectral decomposition Singular value decomposition