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## Homework Statement

A bookie will pay you 6$ for every 1$ bet if you correctly select the winners (adjusted by a spread) in three games. What is the bookies expected earnings? (spread is how much the team wins by, and, when added to the underdog's score, should result in a tie)

## Homework Equations

E[x]=sum(x*f(x))

## The Attempt at a Solution

I'm having trouble getting started and making a probability density function for this because I don't really know how to deal with "the spread". If there was no spread would the pdf look like this?:

X=number of winners selected........money earned by bookie.......probability

0.................................................... $3.............................. 1/8

1.................................................... $-3...............................3/8

2................................................... $-9................................3/8

3.....................................................$-15...............................1/8

and then his expected earnings for this would be 3*(18)+(-3)*(3/8)+(-9)*(3/8)+(-15)*(1/8)