Practice Problems 6

# Practice Problems 6 - Practice Problems 6 1. A gas station...

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Practice Problems 6 1. A gas station sells three grades of gasoline: regular unleaded, extra unleaded, and super unleaded. These are priced at \$1.55, \$1.70, and \$1.85 per gallon *, respectively. Let X 1 , X 2 , and X 3 denote the amounts of these grades purchased (gallons) on a particular day. Suppose the X i ’s are independent with μ 1 = 1,000, μ 2 = 500, μ 3 = 300, σ 1 = 100, σ 2 = 80, and σ 3 = 50. If the X i ’s are normally distributed, what is the probability that revenue exceeds … a) \$2,600? b) \$3,000? 2. Suppose that the actual weight of "10-pound" sacks of potatoes varies from sack to sack and that the actual weight may be considered a random variable having a normal distribution with the mean of 10.2 pounds and the standard deviation of 0.6 pounds. Similarly, the actual weight of "3-pound" bags of apples varies from bag to bag and that the actual weight may be considered a random variable having a normal distribution with the mean of 3.15 pounds and the standard deviation of 0.3 pounds. A boy-scout troop is planning a camping trip. If the boy-scouts buy 3 "10-pound" sacks of potatoes and 4 "3-pound" bags of apples selecting them at random, what is the probability that the total weight would exceed 42 pounds? 3. Let X 1 and X 2 be independent with normal distributions N ( 6, 1 ) and N ( 7, 1 ), respectively. Find P ( X 1 > X 2 ). Hint: Write P ( X 1 > X 2 ) = P ( X 1 – X 2 > 0 ) and determine the distribution of X 1 – X 2 . 4. Compute P ( X 1 + 2 X 2 – 2 X 3 > 7 ), if X 1 , X 2 , X 3 are iid with common distribution N ( 1, 4 ). ______________________________________________________________________________ * This problem was written long time ago.

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5. Suppose that X and Y are i.i.d. ( independent, identically distributed ) with the p.m.f. p ( k ) = ( ) ! 2 ln k k , k = 1, 2, 3, … . Find the
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## This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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Practice Problems 6 - Practice Problems 6 1. A gas station...

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