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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?


Solution Summary

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