Suppose that bus loads for a certain bus route fluctuate randomly throughout theday. Each bus can be classified as either “packed” or “light”, and there is equal likelihoodthat a given bus is one or the other. Suppose a packed bus carries about 80 students perbus on average. A light bus carries about 20 students on average. To decide whether toincrease the number of busses on that route, Transportation Services decides to use Poissondistributions to model this route.(a) Find the PMF of X = # of students on the next PACKED bus on this route.(b) Find the PMF of Y = # of students on the next LIGHT bus on this route.(c) What is the probability that the next bus will have exactly 35 students init? (Hint: The PMFs you calculated in Parts A and B are conditional PMFs given thenext bus’ type.)

Suppose that bus loads for a certain bus route fluctuate randomly throughout theday. Each bus can be classified as either “packed” or “light”, and there is equal likelihoodthat a given bus is one or the other. Suppose a packed bus carries about 80 students perbus on average. A light bus carries about 20 students on average. To decide whether toincrease the number of busses on that route, Transportation Services decides to use Poissondistributions to model this route.(a) Find the PMF of X = # of students on the next PACKED bus on this route.(b) Find the PMF of Y = # of students on the next LIGHT bus on this route.(c) What is the probability that the next bus will have exactly 35 students init? (Hint: The PMFs you calculated in Parts A and B are conditional PMFs given thenext bus’ type.)

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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