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.

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.