(a) If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv's x,,..., X40 and use a rule of expected value.] min (b) What is the variance of your total waiting time? (Round your answer to two decimal places.) min?
(a) If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv's x,,..., X40 and use a rule of expected value.] min (b) What is the variance of your total waiting time? (Round your answer to two decimal places.) min?
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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Please solve (a) & (b) only!
![**Transcription for Educational Website:**
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Suppose your waiting time for a bus in the morning is uniformly distributed on \([0, 10]\), whereas waiting time in the evening is uniformly distributed on \([0, 12]\) independent of morning waiting time.
(a) If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv’s \(X_1, \ldots, X_{10}\) and use a rule of expected value.]
\[\_\_\_\_\_\_\] min
(b) What is the variance of your total waiting time? (Round your answer to two decimal places.)
\[\_\_\_\_\_\_\] min\(^2\)
(c) What are the expected value and variance of the difference between morning and evening waiting times on a given day? (Use morning time – evening time. Round the variance to two decimal places.)
Expected value \[\_\_\_\_\_\_\] min
Variance \[\_\_\_\_\_\_\] min\(^2\)
(d) What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week? (Use morning time – evening time. Assume a week includes only Monday through Friday.)
Expected value \[\_\_\_\_\_\_\] min
Variance \[\_\_\_\_\_\_\] min\(^2\)
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Transcribed Image Text:**Transcription for Educational Website:**
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Suppose your waiting time for a bus in the morning is uniformly distributed on \([0, 10]\), whereas waiting time in the evening is uniformly distributed on \([0, 12]\) independent of morning waiting time.
(a) If you take the bus each morning and evening for a week, what is your total expected waiting time? (Assume a week includes only Monday through Friday.) [Hint: Define rv’s \(X_1, \ldots, X_{10}\) and use a rule of expected value.]
\[\_\_\_\_\_\_\] min
(b) What is the variance of your total waiting time? (Round your answer to two decimal places.)
\[\_\_\_\_\_\_\] min\(^2\)
(c) What are the expected value and variance of the difference between morning and evening waiting times on a given day? (Use morning time – evening time. Round the variance to two decimal places.)
Expected value \[\_\_\_\_\_\_\] min
Variance \[\_\_\_\_\_\_\] min\(^2\)
(d) What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week? (Use morning time – evening time. Assume a week includes only Monday through Friday.)
Expected value \[\_\_\_\_\_\_\] min
Variance \[\_\_\_\_\_\_\] min\(^2\)
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