E6.+Compute+the+expected+value+(aka+mean,+aka+fair+price)+of+a+probability+distribution.

=**E6) Expected Value**=

- Expected Value or fair price is what you are expected to win from any given game of chance. It also allows you to find the estimated fair price that you should be charged for that game if you are going to want to make any money or break even. The Expected value allows for you to find out your chances of succeeding in a situation of chance and how much you will succeed. It also gives you the fair price of that situation or game.
 * 1. What you need to understand.**

- The expected value is the sum of (all the x values multiplied by the probability of getting that x value.) - Σ of x*p(x)= expected value.
 * x || (x) || x*p(x) ||
 * sum || = ||  ||
 * sum || = ||  ||
 * sum || = ||  ||
 * sum || = ||  ||

This is where you write an example of a problem that would assess this indicator. This could be: - Say you are playing a 1 die dice game, and whatever you role is the amount you win in dollars, what is the expected value of this game. - There is an example of how it works.
 * 2. Example problem.**

- Say there is a scratch ticket with ten boxes, with five different, possible prizes that you could get. You are only allowed to scratch off one box though. There is 1 box with $0, 4 boxes with $1, 2 boxes with $2, 2 boxes with $3, and 1 box with $5. What is the expected value of this ticket? Say the store charges 3 dollars for this ticket, what is the fair price that they should charge for you to win any money? - Try to figure it out then look at the link below. [|expected value 2.pages]

- The expected value does not have to equal 1. That is a common misconception that is made among many people. So in the table the second column all equals out to 1, but the third column does not have to equal 1 or any whole number. In fact your expected value can be a decimal even. - Just because there might be a higher probability of getting a prize, that doesn't always mean that that prize has the highest expected value. - In the problem above there are 4 boxes with $1 but there is a higher expected value for the $3 prize
 * 3. Common mistakes or misunderstandings:**

__http://quizlet.com/5766983/e6-expected-value-flash-cards/__ __http://www.math.uah.edu/stat/expect/index.xhtml__ - There are two websites that might help you to understand better. - You could also check pages 545-559 for more information which is in unit 8 lesson 2 of your text book. __http://quizlet.com/1874403/the-expected-value-of-a-random-variable-or-a-function-of-a-random-variable-flash-cards/__ - The third link is partly related and is harder to understand.
 * 4. For more information:**