Question 4: (15 marks)
(10 marks) Let X1, X2, ..., Xn be a random sample from a distribution with the density
f(x; p) = (x + 7) exp(-p) / 8
Conduct a maximum likelihood estimation for the unknown parameter p and derive the maximum likelihood estimate j. (You need to show all the work.)
(5 marks) It is established in the textbook that given a normal distribution, the sample mean X is an unbiased estimate for μ. Prove or disprove that X is also an unbiased estimate for p.