practice midterm, no solutions, please help!

Q4 (14 points) In modelling the number of students that passed by the intersection of University and Philip Street in 1 minute, the Poisson distribution can be used. (a) [2 marks] If the students arrive at random at the rate of 0 per minute, write down the probability mass function of y student passing by the intersection in 1 minute. Remember to write down all assumptionsof the parameters. (b) [3 marks] Suppose y1 , J22, y\" is an observed from n independent 1-minute interval, find the likelihood function L(6). (c) [6 marks] Show that the maximum likelihood estimate of 9 is _ _ 1 n y _ E 2121 3'1" For the following questions, you may assume that 9 = j). (d) [1 mark] Suppose in 10 separate 1-minute interval, the number of student observed were 5, 0, 0,1, 2, 0, 3, 2,1, 0. Find the MLE of 6, Le. 2: based on the provided data. (e) [2 marks] Based on the provided data in (d), estimate the probability that during a one-minute interval, more than 1 student cross the inter