Need help with understanding and solving below question, check attached image for the complete question, I do no intend to submit the tutor's work as my own but since I am completely new to this I would like to understand and then again attempt on my own referring to the solutions. Please help.

3. In this exercise you are going to derive the ML and MAP estimates for the exponential distribution. Recall that a random variable X follows the exponential distribution if its pdf is given by felt | A) = Aexp(-tA) Recall also that this distribution is useful for modeling "waiting time" for an event to happen (such as arrival of a bus, or arrival of a customer to store, or a hit to a website), where the arrivals are independent of each other and the rate of arrival (here A) is fixed. So > is the number of arrivals per unit of time. As a result, B = - is the average waiting time for the first arrival. You know that E(X) = B = X. 3a) Fatma assumes that waiting time for her bus in the morning follows approximately the exponen- tial distribution. She wishes to estimate the rate A through the maximum likelihood method She records for N days arrival times of t1, t2, ..., t. Write down the likelihood function for these observations, clearly indicating what are the variables, and what are known constants. 3b) Write down the algebraic expression for the log likelihood function. 3c) Find the ML estimation AML from the log likelihood function. Show your work. 3d) You are now going to develop the Bayesian maximum posterior likelihood function. First you need to encode the prior degree of knowledge or ignorance about A through a probability distribution. To this end we can assume that our prior estimate of A is given by Ap, and we encode our confidence about this by thinking that we have made ap "virtual" observations and from these observations we arrived at Ap estimate. (For now we assume that