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Unformatted text preview: PROBABILITY I Practice Final Exam August 12, 2008 1. There are 15 white and 3 black balls in an urn. (a) If you draw 2 balls randomly (without replacement), what is the probability that both are black? (b) If you draw 10 balls randomly (with replacement), what is the probability that 8 of them are black? (c) Estimate this probability using the Poisson distribution. (d) Again, if you draw 10 balls randomly (with replacement), what is the expected number of turnovers (black balls followed by white or white balls followed by black) (e) Now assume that you draw balls (again with replacement) until a black ball is drawn (i.e. you are not restricted to 10 drawings). What is the expected number of drawings needed to obtain a black ball? 2. The newspaper says my movie begins at 8 pm, and I seem to be late. The length of the previews is a continuous random variable that I estimate is given by the probability density f X ( x ) = K x 2- x 2 , for 0 < x < 1 / 2 . (1) and the length of the movie is a continuous random variable with...
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