An optical device is used to detect the passage of cars in a single lane of a downtown street. Because there must be at least half a second between successive cars, it is assumed that the times T; between cars are of the form T; = 0.50 + Si, where S1, S2, · . are independent exponential (A) random variables. (a) Find the mean and variance of each T;. (h) Let y be the time ot which the nth cor possec the detector Coleulote the meon ond vorionce of
An optical device is used to detect the passage of cars in a single lane of a downtown street. Because there must be at least half a second between successive cars, it is assumed that the times T; between cars are of the form T; = 0.50 + Si, where S1, S2, · . are independent exponential (A) random variables. (a) Find the mean and variance of each T;. (h) Let y be the time ot which the nth cor possec the detector Coleulote the meon ond vorionce of
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:6. An optical device is used to detect the passage of cars in a single lane of a downtown street. Because
there must be at least half a second between successive cars, it is assumed that the times T; between
= 0.50 + Si, where S1, S2, ··. are independent exponential (A) random
cars are of the form T;
variables.
(a) Find the mean and variance of each T;.
(b) Let Y, be the time at which the nth car passes the detector. Calculate the mean and variance of
Yn.
(c) Under what conditions is Yn approximately normally distributed and why?
(d) When n =
50 and A = 0.10, calculate the approximate probability that Yn exceeds 500 seconds.
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