6. An optical device is used to detect the passage of cars in a single lane of a downtown street. Becausethere 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) randomcars 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 ofYn.(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.

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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