b) A social media agency would like to study the average amount of time a visitor spends on accessing an online platform. Based on some analyses on the past data, it is believed that the amount of time a visitor spends on accessing the platform follows an exponential distribution with a rate parameter 0, where 0 > 0. Let be the expected amount of time a visitor spends on accessing the platform. Then it is known that 0 = 1. The agency conducts a survey to interview five visitors and asks them the amount of time they spend on the platform. Let Ti, T2, 73, Ta, T's be the amounts of time the five visitors spend on the platform which are measured in hours. Suppose that Ti, 72, 73, Ta, Is are independent and identically distributed random variables with each following an exponential distribution with a rate parameter 0. It is also assumed that the following sample data are collected from the survey. 71 = 0.2, 72 = 0.25, T3 = 1.8, TA = 0.75, T, = 1.5. Based on the above assumptions, answer the questions in (i)-(ii) as follows: (i) Calculate the method of moments estimate for f. (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 u