We are interested in estimating the average number of tattoos that UNL students have. We randomly select 76 UNL students, and ask them how many tattoos they have. The total number of tattoos among these 76 students is 21.

a. Explain why this scenario can be modeled using a Poisson distribution. Your explanation should also include in words what n, X_1, X_n, lambda, and x_1, , x_n are in this situation, and, if applicable, give the numerical values of each.
b. Find the UMVU-Estimator (UMVUE) and UMVU-Estimate for lambda. Show and explain ALL WORK.
c. We are also interested in estimating lambda e^-lambda. In words, what probability can we represent using lambda e^-lambda? Find the UMVUE for lambda e^-lambda, well as the UMVU-Estimate for lambda e^-lambda. Show and explain all work.