prac311mid02

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

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Unformatted text preview: 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( ) distribution. Suppose the probability that each day a young boy captures a prairie dog at a certain place is , and Y is the number of days until the young boy captures the first prairie dog. Find simple formulas in terms of and for the following probabilities. (The formulas should not involve an infinite sum.)probabilities....
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prac311mid02 - STAT311 Practice Questions II Question 1 An...

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