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Stat 5131 (Geyer) Final Exam Solutions

# Stat 5131 (Geyer) Final Exam Solutions - Up Stat 5131 Stat...

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Up: Stat 5131 Stat 5131 Final Exam Problem 1 The probability of rolling a six with one die is 1 / 6. Since the dice are statistically independent, the probability of a double six is (1 / 6) 2 = 1 / 36. X is the waiting time until the first double six, hence it is a geometric random variable with success probability p = 1 / 36. (a) (b) so Problem 2 Let X be the number of calls. Then ,where .The normal approximation is .What we are to calculate is .The normal approximation with continuity correction for this is P ( Y > 115.5), where . This is Not part of the problem, but just for the record, the exact probability is .

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Problem 3 (a) The number of oak trees X is distributed where A is the area of the rectangle, or 0.32 hectare. Hence the mean of X is . Then (b) Again, the number of oak trees X is distributed where now A is the area of the circle or hectares. Hence the mean of X is (c) As with any Poisson random variable so .In this case . Problem 4 For the relevance of this calculation to analyzing lottery results see my web page on analyzing the lottery .
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