Lana arrives at a bus stop at a uniformly random time. When Lana arrives at the bus stop, either of two independent bus lines (both of which can take her school) may come by. Company A’s bus arrival times are exactly 10 minutes apart, whereas the time from one Company B bus to the next is distributed as Expo (1/10) .What is the probability that Company B’s bus arrives first?What is the PDF of Lana ‘s waiting time for a bus? Be sure to state what the support of the distribution is.Write a simulation to check that your answer in part (1) and your expression for the PDF in part (2) are correct.Answer the following:What is the probability that Company B’s bus arrives first?What is the PDF of Lana ‘s waiting time for a bus? Be sure to state what the support of the distribution is.Write a simulation to check that your answer in part (1) and your expression for the PDF in part (2) are correct.(Solve by hand)use python code when needed!

Answered: Lana arrives at a bus stop at a…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Lana arrives at a bus stop at a uniformly random time. When Lana arrives at the bus stop, either of two independent bus lines (both of which can take her school) may come by. Company A’s bus arrival times are exactly 10 minutes apart, whereas the time from one Company B bus to the next is distributed as Expo (1/10) .

What is the probability that Company B’s bus arrives first?
What is the PDF of Lana ‘s waiting time for a bus? Be sure to state what the support of the distribution is.
Write a simulation to check that your answer in part (1) and your expression for the PDF in part (2) are correct.

Answer the following:

What is the probability that Company B’s bus arrives first?
What is the PDF of Lana ‘s waiting time for a bus? Be sure to state what the support of the distribution is.
Write a simulation to check that your answer in part (1) and your expression for the PDF in part (2) are correct.

(Solve by hand)

use python code when needed!

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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