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problemset35 - STAT/MA 416 Problem Set 35 Name 1 Jim cuts...

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STAT/MA 416 November 28, 2011 Problem Set 35 Name: 1. Jim cuts wood planks of length X for customers, where X is uniformly distributed between 10 and 14 feet. The price of a piece of wood is $2 per foot, plus a flat-rate surcharge of $2 for Jim’s services. So Y = 2 X + 2 is the amount he charges for a piece of wood. a. Find the density f Y ( y ). Be sure to specify the interval where f Y ( y ) is nonzero. b. Using the density f Y ( y ) of Y , find the probability that Y exceeds $28. c. Check your answer: Using the density f X ( x ) of X , find the probability that Y = 2 X + 2 exceeds $28. 1
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2. Let X be the price of a CD during a “lightning sale” on Cyber Monday. The total purchase price (in dollars) is Y = 1 . 07 X + 3 . 99, since there is 7% tax and $3.99 shipping. Suppose that X is uniform on the interval [4 , 9]. a. Find the density f Y ( y ). Be sure to specify the interval where f Y ( y ) is nonzero. b. Find the expected purchase price (with tax and shipping) by E ( Y ) = R y f Y ( y ) dy .
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