Chapt 4f - 4.14 Problems 161 the gas station, what is the...

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4.14 Problems 161 the gas station, what is the probability that a waiting line will occur at the station? 4.38 The number of trafFc tickets that a certain trafFc ofFcer gives out on any day has been shown to have a Poisson distribution with a mean of 7. a. What is the probability that on one particular day the ofFcer gave out no ticket? b. What is the probability that she gives out fewer than 4 tickets in one day? 4.39 A Geiger counter counts the particles emitted by radioactive material. If the number of particles emitted per second by a particular radioactive ma- terial has a Poisson distribution with a mean of 10 particles, determine the following: a. The probability of at most 3 particles in one second. b. The probability of more than 1 particle in one second. 4.40 The number of cars that arrive at a drive-in window of a certain bank over a 20-minute period is a Poisson random variable with a mean of four cars. What is the probability that more than three cars will arrive during any 20- minute period? 4.41 The number of phone calls that arrive at a secretary’s desk has a Poisson distribution with a mean of 4 per hour. a. What is the probability that no phone calls arrive in a given hour? b. What is the probability that more than 2 calls arrive within a given hour? 4.42 The number of typing mistakes that Ann makes on a given page has a Pois- son distribution with a mean of 3 mistakes. a. What is the probability that she makes exactly 7 mistakes on a given page? b. What is the probability that she makes fewer than 4 mistakes on a given page? c. What is the probability that Ann makes no mistake on a given page? Section 4.8: Exponential Distribution 4.43 The PD± of a certain random variable T is given by f T ( t ) = ke - 4 t t 0 a. What is the value of k ?
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162 Chapter 4 Special Probability Distributions b. What is the expected value of T ? c. Find P [ T < 1 ] . 4.44 The lifetime X of a system in weeks is given by the following PDF: f X ( x ) = b 0 . 25 e - 0 . 25 x x 0 0 otherwise a. What is the expected value of X ? b. What is the CDF of X ? c. What is the variance of X ? d. What is the probability that the system will not fail within two weeks? e. Given that the system has not failed by the end of the fourth week, what
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This note was uploaded on 01/05/2010 for the course STAT 350 taught by Professor Carlton during the Fall '07 term at Cal Poly.

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Chapt 4f - 4.14 Problems 161 the gas station, what is the...

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