IAI CT4 OCT 2015 Q8

Solution given is:
Is not the given solution for the exponential distribution? Question asks for Poisson distribution...someone please clarify...

 

From the data, there is one death at age 50 last birthday (Life J) and the total central exposed to risk at age 50 last birthday is 4.75 years. So the likelihood function is P(D=1), where D ~Poi(4.75 mu). This is as shown in the solution.

I do have an issue with this question though - it should ask for the ML estimate, not the ML estimator. The estimator is a random variable.

 

Thank you.