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Stat341S07Practice Exam2

# Stat341S07Practice Exam2 - Practice Exam2-Stat341 1 The...

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Practice Exam2—Stat341 1) The probability that an aircraft that disappeared from radar will be discovered is 0.70. Of the aircraft that are discovered, 60% have an emergency locator. Of the aircraft that are not discovered, 90% do not have such a locator. Suppose an aircraft has disappeared. If it does not have an emergency locator then what is the probability that it will be discovered? 2) Let X be a discrete random variable that can assume the values: 0,1,2,3,4. a) Which of the following three functions are legitimate p.m.f for X, and why are the other two not allowed? x 0 1 2 3 4 _________________________________________ f(x) .3 .2 .1 .05 .05 _________________________________________ f(x) .4 .1 .1 .1 .3 _________________________________________ f(x) .4 .1 .2 .1 .3 _________________________________________ b) For the legitimate p.m.f of part (a), find the Distribution function and compute P(2 < X < 4) and P(X = 0). 3) Let X have the probability distribution function, p(x) = (x+2)/25, for x = 1,2,3,4,5. i. Find P(X 2). (2 pts) ii. Find P(X = 5). (2 pts) iii. Find F(x) for - < x < . (3 pts) iv. Find E(X), E(X 2 ) and σ 2 . (6 pts) v. Use your answer to part (iv) to find E[(2X+1) 2 ]. (3 pts) vi.

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