A tree ecologist is studying oak trees in a forest in upstate New York. She knows from prior research

that oaks occur at a rate of 8.2 trees per square mile in this forest. She marks off a random one-squaremile

region in the forest, and a research assistant will count the number of trees in that region. Let Y

be the random variable representing the number of trees counted.

a) [2 points] 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) [2 point] Calculate the expected value and standard deviation of Y .

c) [3 points] What is the probability that she counts 10 trees?

d) [3 points] Her research assistant stops to take a break and reports that she's counted four trees so

far, so Y 4 . Knowing this, what is the probability that after she finishes counting, she has counted

Y = 10 trees, that is P(Y = 10|Y 4) ?

e) [2 points] 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) ?