fall08-realquiz3

# fall08-realquiz3 - PROBABILITY AND DECISION MAKING 45-730...

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PROBABILITY AND DECISION MAKING 45-730 REAL QUIZ 3 (OFFLINE) Problem 1 ( pdf and cdf ) . Let X be a continuous random variable with pdf f ( x ) and cdf F ( x ). Suppose also that f ( x ) = x 3 9 for 0 x A and zero everywhere else. a) Find the value of A. b) Compute the formula for F(x). c) What is the median of this distribution ? d) What is the mean of this distribution ? e) Find the 75th percentile of this distribution, i.e., the value B such that F ( B ) = 0 . 75. Problem 2 ( Uniform and Triangular distributions ) . Suppose you are participating in a reverse auction where you face two competitors: One is bidding from a symmetric triangular distribution in the range from zero to 1 million dollars, while the other’s bid is uniformly distributed in the same range, independent of ﬁrst one’s bid. a) What is the cdf F ( x ) for the random variable X denoting the value of the maximum competing bid (among your two competitors)? b) Suppose you want to make a bid that has a 50% chance of success of being the winning (maxi- mum) bid among the three bids submitted. Should the amount you bid be half a million dollars? If not, what should it be? Problem 3 ( Uniform and Triangular distributions ) . The maximum temperature on a particular day is predicted to be uniformly distributed in the range 60 F to 72 F . a) What is the probability that the maximum temperature will be greater than 68 F ? b) What is the mean of this distribution ?

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## This note was uploaded on 10/05/2010 for the course BUS 45730 taught by Professor Ravi during the Spring '08 term at Carnegie Mellon.

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fall08-realquiz3 - PROBABILITY AND DECISION MAKING 45-730...

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