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econ41class9_practice_problems

econ41class9_practice_problems - Econ 41 Ekaterini...

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Econ 41 Ekaterini Kyriazidou UCLA Statistics for Economists Class 9: Practice Problems
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On Independent and Mutually Exclusive events (Problem 14, Page 183) There are 200 graduate students, out of which 110 female and 125 out-of-state. Of the 110 female students 70 are out-of-state. If one student is selected at random what is the probability that the student is a male? P ( male ) = 1 P ( female ) = 1 110 / 200 . If one student is selected at random what is the probability that the student is out-of-state given that it’s a female? P ( out-of-state | female ) = 70 / 110 . Are the events "female" and "out-of-state" independent? P ( out-of-state ) = 125 / 200 6 = P ( out-of-state | female ) = 70 / 110 . Not independent. Are they mutually exclusive? No, they can occur together.
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(Problem 19, Page 183) The probability that a randomly selected student from a college is female is .55 and that a student works for more than 10 hours per week is .62. If these two events are independent, fi nd the probability that a randomly selected student is Male and works for more that 10 hours per week. By independence, P ( M and W ) = P ( M ) · P ( W ) Female or works for more than 10 hours per week. By addition rule, P ( F or W ) = P ( F ) + P ( W ) P ( F and W ) = P ( F ) + P ( W ) P ( F ) P ( W ) Note: F and W are not mutually exclusive but they are independent.
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