Suppose that the distribution of time at a single job is a gamma distribution with a mean of $5$ years and a standard deviation of $2$ years, and suppose that the times at successive jobs are i.i.d. random variables. Every year the person fills out the survey. What are the approximate average answers to the following questions:
a. How long have been working at your current job?
b. How long did you work at your last job?
My attempt: (b) From the given information, the average time spent at the last job should follow gamma distribution with mean $5$ years, so the answer should be $\fbox{5}$ years?
(a) Let $Y_i =$ the time spent at current job. Then it also follows gamma distribution, so $E(Y_i) = 5$ years. Let $T_i = $ transition time from the last job to the current job are random variable, but we are not given $E(T_i)$. How could we solve this part?
My question: I don't see the difference between the two questions, as in both cases, the question seems not to account for the transition time. Also, we are not given the average transition time between successive jobs. Could someone please help with the correct interpretation?