1. When the 6 or 8 bus arrives at the university, the next bus arrives after Exp(1/4) time (units are in hours). (a) What is the expected number of buses that arrive in a two-hour period? [1 mark] (b) What is the probability that at least two buses arrives in a 10 minute period. [1] (c) Consider the 6 consecutive 10 minute periods between 3pm and 4pm. What is the probability that at least one of these periods has two or more buses arriving in it? [2] (d) I arrive at the bus stop and start my watch. What is the expected amount of time until the sixth bus arrives. What is the standard deviation of this time? [2] (e) Rush hour traffic limits the number of buses arriving. Given that exactly two buses arrive between 8:30am and 9:30am, what is the expected arrival time of the second bus? [3] (f) I want to get the number 6 bus. Each bus that arrives is a number 6 bus independently with probability 0.25. What is the expected amount of time to wait until a number 6 bus? [1]
1. When the 6 or 8 bus arrives at the university, the next bus arrives after Exp(1/4) time (units are in hours). (a) What is the expected number of buses that arrive in a two-hour period? [1 mark] (b) What is the probability that at least two buses arrives in a 10 minute period. [1] (c) Consider the 6 consecutive 10 minute periods between 3pm and 4pm. What is the probability that at least one of these periods has two or more buses arriving in it? [2] (d) I arrive at the bus stop and start my watch. What is the expected amount of time until the sixth bus arrives. What is the standard deviation of this time? [2] (e) Rush hour traffic limits the number of buses arriving. Given that exactly two buses arrive between 8:30am and 9:30am, what is the expected arrival time of the second bus? [3] (f) I want to get the number 6 bus. Each bus that arrives is a number 6 bus independently with probability 0.25. What is the expected amount of time to wait until a number 6 bus? [1]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. When the 6 or 8 bus arrives at the university, the next bus arrives after Exp(1/4) time (units are in hours).
(a) What is the expected number of buses that arrive in a two-hour period? [1 mark]
(b) What is the probability that at least two buses arrives in a 10 minute period. [1]
(c) Consider the 6 consecutive 10 minute periods between 3pm and 4pm. What is the probability that at
least one of these periods has two or more buses arriving in it? [2]
(d) I arrive at the bus stop and start my watch. What is the expected amount of time until the sixth bus
arrives. What is the standard deviation of this time? [2]
(e) Rush hour traffic limits the number of buses arriving. Given that exactly two buses arrive between
8:30am and 9:30am, what is the expected arrival time of the second bus? [3]
(f) I want to get the number 6 bus. Each bus that arrives is a number 6 bus independently with probability
0.25. What is the expected amount of time to wait until a number 6 bus? [1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d8b8c35-fcea-418b-8926-d475acc1096c%2Fc7552063-8add-465f-aafa-fde341f423af%2Fqh8m0ggi_processed.png&w=3840&q=75)
Transcribed Image Text:1. When the 6 or 8 bus arrives at the university, the next bus arrives after Exp(1/4) time (units are in hours).
(a) What is the expected number of buses that arrive in a two-hour period? [1 mark]
(b) What is the probability that at least two buses arrives in a 10 minute period. [1]
(c) Consider the 6 consecutive 10 minute periods between 3pm and 4pm. What is the probability that at
least one of these periods has two or more buses arriving in it? [2]
(d) I arrive at the bus stop and start my watch. What is the expected amount of time until the sixth bus
arrives. What is the standard deviation of this time? [2]
(e) Rush hour traffic limits the number of buses arriving. Given that exactly two buses arrive between
8:30am and 9:30am, what is the expected arrival time of the second bus? [3]
(f) I want to get the number 6 bus. Each bus that arrives is a number 6 bus independently with probability
0.25. What is the expected amount of time to wait until a number 6 bus? [1]
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