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Statistics / Introduction to Probability 1 / Chapter 9 / Problem 1

Introduction to Probability | 1st Edition | ISBN: 9781466575578 | Authors: Joseph K. Blitzstein, Jessica Hwang

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Fred wants to travel from Blotchville to Blissville, and is deciding between 3 options

Chapter 9, Problem 1

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QUESTION:

Fred wants to travel from Blotchville to Blissville, and is deciding between 3 options (involving dierent routes or dierent forms of transportation). The jth option would take an average of j hours, with a standard deviation of j hours. Fred randomly chooses between the 3 options, with equal probabilities. Let T be how long it takes for him to get from Blotchville to Blissville. (a) Find E(T). Is it simply (1 + 2 + 3)/3, the average of the expectations? (b) Find Var(T). Is it simply (2 1 + 2 2 + 2 3)/3, the average of the variances.

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QUESTION:

Fred wants to travel from Blotchville to Blissville, and is deciding between 3 options (involving dierent routes or dierent forms of transportation). The jth option would take an average of j hours, with a standard deviation of j hours. Fred randomly chooses between the 3 options, with equal probabilities. Let T be how long it takes for him to get from Blotchville to Blissville. (a) Find E(T). Is it simply (1 + 2 + 3)/3, the average of the expectations? (b) Find Var(T). Is it simply (2 1 + 2 2 + 2 3)/3, the average of the variances.

ANSWER:

Step 1 of 3

Given that,

Fred decides to travel from Blotchville to Blissville, and is deciding between 3 options (involving different routes or different forms of transportation). The option would take an average of hours, with a standard deviation hours. Fred randomly chooses between the 3 options, with equal probabilities. Let be how long it takes for him to get from Blotchville to Blissville.

Fred is deciding between 3 choices.

Defining with equal probabilities respectively.

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