(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?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section: Chapter Questions
Problem 59RE
Question

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\(^2\)

--- 

There are no graphs or diagrams in this image.
Transcribed Image Text:**Transcription for Educational Website:** --- 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\(^2\) --- There are no graphs or diagrams in this image.
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