# 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?

https://brainmass.com/math/recurrence-relation/probability-moment-generating-functions-150936

#### Solution Summary

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