Red Maple trees occur at a rate of 8.2 trees per square mile in a forest. A researcher marks off a random one-square-mile region in the forest, and his research assistant will count the number of Red Maple trees in that region. Let Y be the random variable representing the number of Red Maple trees counted.

a. What probability distribution is appropriate to model the random variable Y? (justify your answer, be sure to give the name of the distribution and the values of its parameter).

b. Calculate the expected value and standard deviation of Y.

c. What is the probability that the research assistant counts 10 trees?

d. The research assistant stops to take a break and reports that she's counted four trees so far, soY4. Knowing this, what is the probability that after she finishes counting, she has counted Y= 10trees, that is P(Y= 10|Y4)?

e. In the course of the experiment, two tags are left on each tree. Let X= 2Y denote the total number of tags used in the experiment. What is Var(X)?