### Expected Value of a Discrete Function

• Understand conditions for discrete probability distribution function.

• Calculate the expected value of a discrete function.

$E(X) = \Sigma x_i P(x_i)$

### Solved Example:

#### 9-2-01

You pick 3 different numbers between 1 and 9. If you pick all the numbers correctly you win \$50. What are your expected earnings if it costs \$1 to play?

Solution:
Probability of winning, $P(\mathrm{Winning\ \$49}) = \dfrac{1}{({}^{9}C_{3})} = \dfrac{1}{84}$Probability of losing,$P(\mathrm{Losing\ \$1}) = 1- \dfrac{1}{84} = \dfrac{83}{84}$