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Probability: Moment-Generating Functions

The moment-generating function
Please solve for only #3.1.
I am attaching 2-5_14.doc, please take a look when you work on #3.1.
I think there are two questions in the problem. Please explain each step of your solutions for each part.

3.1 How to stress out Coach
A college hires a new football coach on the terms that if the team loses two games in a row than he's fired. Assume that the probability of a team winning any of their games is 0.5. How many games do you expect that the Coach will keep his job? You will find question 2.5-14 on page 111 helpful. If the teams probability of winning a game is 0.8 (for every game they play), then how many games would you expect the coach to hold onto his job?

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Solution Summary

This solution looks at calculating the moment generating function, formatted step by step with explanation in an attached PDF.

$2.19