Question
17. A tree ecologist is studying oak trees in a forest in upstate New York. She knows from prior research that oaks occur at a
17. 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) ?
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