problemset27

# problemset27 - b. Find the variance of the cost of your...

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STAT/MA 416 October 31, 2011 Problem Set 27 Name: 1. Suppose that X has CDF F X ( x ) = 0 x < 2, x - 2 4 2 x 6, 1 x > 6. a. Find P ( X 4 . 5). b. Find P (3 . 09 X 4 . 39). c. Find P ( X 3 . 7). 1

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2. Assume that the amount of soda in a can is uniformly distributed between 11.93 ounces and 12.02 ounces. a. What is the probability that it has more than the stated quantity that is printed on the can, which is 12 ounces? b. What is the standard deviation of the amount (in ounces) of soda in the can? (Remember that the standard deviation is the square root of the variance.) 2
3. Suppose that, when you buy gas at the gas station, the price is uniformly distributed between \$4.30 and \$4.50 per gallon. You plan to buy 12 gallons of gasoline, plus a candy bar for an extra \$1.00. (Assume that there is no tax on your purchase.) a. Find the expected value of the cost of your purchase.

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Unformatted text preview: b. Find the variance of the cost of your purchase. 3 4. Let X,Y,Z be independent and uniformly distributed on the interval [0 , 10]. Find the probability that Y is the middle value, i.e., nd P ( X &lt; Y &lt; Z or Z &lt; Y &lt; X ). 4 5. Suppose X,Y have constant joint density on the triangle with vertices at (0 , 0), (3 , 0), and (0 , 3). Find E (min( X,Y )). 5 6. Design your own problem and solution. Create your own problem about one or two uniform continuous random variables. Design your problem in such a way that you would nd it enjoyable and also interesting (i.e., not completely trivial) if you found this problem in a probability book. Please provide the answer for your problem too. 6...
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## This note was uploaded on 02/28/2012 for the course STAT 416 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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problemset27 - b. Find the variance of the cost of your...

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