230hw4. - x x x f 1 1 5 4 what need the capacity of the tank be so that the probability of the supply's being exhausted in a given week is.01 3

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November 21, 2011 MATH 230 HOMEWORK # 4 (Due: November 29, 2011, Tuesday) (Submit your homework to my office till 5:00 pm) (Please, DO NOT forget to write your section number to your homework) 1. Trains headed for destination A arrive at the train station at 15-minute intervals starting at 7:00 in the morning, whereas trains headed for destination B arrive at 15- minute intervals starting at 7:05 in the morning. a) If a certain passenger arrives at the station at a time uniformly distributed between 7:00 and 8:00 in the morning and gets on the first train that arrives, what proportion of time does he/she go to destination A? b) What if passenger arrives at a time uniformly distributed between 7:10 and 8:10 in the morning? 2. A filling station is supplied with gasoline once a week. If its weekly volume of sales in thousands of gallons is a random variable with probability density function < < = otherwise
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Unformatted text preview: x x x f 1 ) 1 ( 5 ) ( 4 what need the capacity of the tank be so that the probability of the supply's being exhausted in a given week is .01? 3. Suppose that the cumulative distribution function of a random variable X is given by 1 ) ( 2 > − = − t e t F t X . Evaluate; a) P( X > 2); b) P ( 1 < X < 3); c) E( X ); d) Var ( X ). 4. Suppose that a system contains a certain type of component whose time in years to failure is given by T. The random variable T is modeled by the exponential distribution with mean time to failure 5 years. If 5 of those components are installed in different systems what is the probability that at least 2 are still functioning at the end of 8 years? 5. The CPU time requirement of a typical program measured in minutes is found to follow a Gamma Distribution with parameters α =3 and β =2.What is the probability that CPU demand of a program will exceed 1 minute?...
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This note was uploaded on 12/22/2011 for the course CS 101 taught by Professor Dat during the Spring '11 term at Bilkent University.

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