Welch/Downloads/Stat%20110%20final%20review.pdf + CO A T 5. For a survey, N participants are recruited, with N - 1 ~ Pois()). (Note that N itself is not Poisson: subtracting 1 from N yields a Poisson. This ensures that N will not be 0, which is good since a survey with no participants is not much of a survey.) Fach participant is asked a yeso question Suppose that each participant answers "yes" with probability p and "no" with probability q = 1 - p, independent of other participants. Let X be the number of participants who answer "yes" and Y be the number who answer "no". So X + Y = N. (a) Find E(N) and Var(N). (b) Find E (~) (c) Find P(X = i, Y = j), where i and j are positive integers. O Ei n 23 S W X