Question 4 (10 marks) a) A marketing analytics firm studies the average number of potential customers visiting a newly introduced online shopping platform per day in a shopping session. Based on some past analysis, it is supposed that (1) potential customers visit the online shopping platform at a constant rate of customers per day on average in the shopping session; (2) potential customers visit the online shopping platform independently. Let N1, N2, N3, N4, N5, N6 be the numbers of potential customers visiting the online shopping platform on six consecutive days. Assume that N1, N2, N3, N4, N5, N6 are independent and identically distributed random variables with the common distribution Poisson(), (i.e., a Poisson distribution with a rate parameter , where > 0). It is also assumed that the following sample data are collected. N1 = 200, N2 = 220, N3 = 368, N4 = 185, N5 = 160, N6 = 235. Based on the above assumptions, answer the questions in (i)-(ii) as follows: (i) Calculate the method of moments estimate for . (2 marks) (ii) Derive the maximum likelihood estimator for by taking the derivative of the log-likelihood function and calculate the maximum likelihood estimate for . (3 marks)