1) Suppose that if a certain virus is present in a population, it will be present the following month with probability 0.8 and if the virus is absent from the population, it will be absent the following month with probability 0.4. If the virus is currently absent from the population, what is the probability that it appears exactly once in the next 2-month period?

2) Letp(1) = 0.06,p(2) = 0.1, andp(3) = 0.95be the probability mass function for a discrete random variableX.

(a)Compute the expected value ofX,E(X).

(b)Compute the variance ofX, Var(X).

3) Consider a population of tigers that grows according topt+1=pt+It, whereptrepresents the number of tigers in yeartand the immigration termItis 20 with a 80% chance and 0 with a 20% chance. Suppose that initially there are 100 tigers and that immigration from year to year is independent. What is the probability that there will be 300 tigers after 10 years?