AMS310 Summer2011 hw4-ch5 solutions(1)

AMS310 Summer2011 - Homework 4(Chapter 5 Solutions 1 Suppose that I take a bus home from my office and that every 5 minutes a bus arrives at SAC

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Homework 4 (Chapter 5) Solutions 1. Suppose that I take a bus home from my office, and that every 5 minutes a bus arrives at SAC. Because of variation in the time that I leave my office, I don’t always arrive at the bus stop at the same time, so my waiting time X for the next bus is a continuous r.v. = . . 0 5 0 5 1 ) ( w o x x f (a) What is the probability of waiting between 1 to 3 minutes? (b) 5 2 5 1 5 3 5 5 1 ) ( ) 3 1 ( 3 1 3 1 3 1 = - = = = = x dx dx x f X P (c) Or 5 2 ) 1 3 ( 5 1 ) 3 1 ( = - = X P . (d) (e) What is the probability of waiting for at least 4 minutes? (f) 5 1 5 4 1 5 5 1 ) 4 ( 5 4 5 4 = - = = = x dx X P . (g) 2. Time until failure (in years) for a circuit board: = - . . 0 0 2 ) ( 2 w o x e x f x

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(a) What is the probability that a circuit board lasts for at least 1 year: 135 . 2 ) ( ) 1 ( 2 1 2 1 2 1 = = - = = = - - - e e dx e dx x f X P x x . (b) What is the probability that a circuit board’s lifetime is between 6 months and 2 years? 350
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This note was uploaded on 09/14/2011 for the course AMS 310 taught by Professor Mendell during the Summer '08 term at SUNY Stony Brook.

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AMS310 Summer2011 - Homework 4(Chapter 5 Solutions 1 Suppose that I take a bus home from my office and that every 5 minutes a bus arrives at SAC

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