(Solved): (b) Assume the time, X, to fix a car is approximately a Gamma distribution with mean = 2 hours a ...

(b) Assume the time, X, to fix a car is approximately a Gamma distribution with mean ? = 2 hours and standard deviation, o = ?2 hours. Find the gamma density function. f(x). Derive, using definition, the moment generating function for X. (1) (ii) (5 marks) (4 marks) (1) Is X a chi-square distribution? If so, state the degrees of freedom for the distribution of X. Otherwise, explain why X is not a chi-square distribution. (2 marks)