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prac311mid02

# prac311mid02 - STAT311 Practice Questions II Question 1 An...

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STAT311 Practice Questions II Question 1 An urn contains 2 white ball and 3 red balls. Two balls are randomly drawn from the urn with replacement. Let X be the number of red balls drawn, and let Y be the draw on which the first red ball is drawn. (For example: the draw WR would give X = 1 and Y = 2.) (a) Give the joint probability (mass) function p X , Y (x , y) of X and Y. (b) Give the probability (mass) function for X and Y: p X (x) and p Y (y). (c) Find E(X * I { Y=2 } ). (d) Are X and Y are independent? (You must give a correct reason for your answer.) Question 2 Suppose that X is the number of prairie dogs found in a square mile of prairie, and it has a Poisson( μ ) distribution. Suppose the probability that each day a young boy captures a prairie dog at a certain place is θ , and Y is the number of days until the young boy captures the first prairie dog. Find simple formulas in terms of μ and θ for the following probabilities. (The formulas should not involve an infinite sum.) (a) P(XY < 3).

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prac311mid02 - STAT311 Practice Questions II Question 1 An...

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