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-square-mile 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). \\vspace {2cm} b) [2 point] calculate the expected value and standard deviation of $Y$. \\vspace{2cm} c) [3 points] what is the probability that she counts 10 trees? \\vspace {3cm} d) [3 points] Her research assistant stops to take a break and reports that she's counted four trees so far, so $Y \\geq 4$. Knowing this, what is the probability that after she finishes counting, she has counted $Y = 10$ trees, that is $P(Y = 10 | Y \\geq 4) $? \\vspace {5cm} 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 \\(\\text{var} (X)\\)