HW7-sol (Math 425) - Math 425 – Section 8 Homework 7 –...

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Unformatted text preview: Math 425 – Section 8 Homework 7 – Chapter 5, problems 1,5,8,10,14,21,23,27,32 Problem 5. A filling station is supplied with gasoline once a week. If its weekly volume of sales in thousands of gallons is a random variable X with p.d.f. f ( x ) = ‰ 5(1- x ) 4 < x < 1 otherwise what need the capacity of the tank be so that the probability of the supply’s being exhausted in a given week is .01? Solution. Let c be the capacity of the tank. We want to find c such that P { X > c } = . 01 We have: P { X > c } = Z 1 c 5(1- x ) 4 dx =- (1- x ) 5 | 1 c = (1- c ) 5 So, 1- c = . 01 1 / 5 , i.e. c = 1- . 01 1 / 5 . Problem 10(a). Trains headed for destination A arrive at the train station at 15 minute intervals starting at 7 A.M., whereas trains headed for destination B arrive at 15 minute intervals starting at 7:05 A.M. If a certain passenger arrives at the station at a time uniformly distributed between 7 and 8 A.M. and then gets on the first train that arrives, what proportion of time does he or she go...
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HW7-sol (Math 425) - Math 425 – Section 8 Homework 7 –...

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