Download 18B Notes.notebook

18B Notes.notebook
May 24, 2016
18B ­ Expected Values
Expected Value or E(X) = mean value of X
(The book calls this expectation)
Look at this as ­Weighted average probability
­Long run average
E(X) = np (In formula packet)
Ex. Roll a die 600 times. Let X = # of 2's rolled.
E(X) = To find E(X) from a probability distribution table, multiply each x and its probability, then add them all together
Ex. 1 X = # of children in a family
Find k
Find E(x)
May 24­10:50 AM
Jan 15­11:33 AM
Ex. 2
Example 1: In a game, you roll a die once. If you get a 1 or a 2, you win nothing but if you roll a 3, 4, 5 or 6, you win $10. Create a probability distribution table for this situation and then find the expected value. Is this a fair game?
You pay $2 to play a game where you draw one colored coin. Drawing one of the 10 red coins gets you $0. Drawing one of the 4 blue coins gets you $3.
If you draw the one gold coin you get $16.
Let X =
x
P(X=x)
Find E(X) for this game.
Would you play this game??
How much should the gold coin be worth to make this game fair?
Jan 13­9:24 AM
Example 2: In a certain carnival game, there are 5 prizes and the
expected value is $8. The first prize is $30 and the probability of
that happening is 2%, the 2nd prize is $10 and the chance of
winning that is 5%, the third prize is $1 and the chance of winning
Jan 9­6:02 AM
Game
Pay $1 to play this game:
Roll a die and then flip a coin.
that is 30%, the 4th prize is $0 and the chance of winning that is
40%.
a. Set up a probability distribution table for this carnival game.
If you get an even number on the die and a head, you win $3.
b. What is the missing probability?
If you get an even number on the die and a tail, you win $1.
c. What is the missing prize amount?
If you get an odd number, you win $0.
d. What would be a good amount for the carnival to charge for this
Do this simulation 25 times and keep track of what you win each time.
game? What would be too much to charge, do you think?
Jan 13­9:26 AM
Jan 10­8:35 PM
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18B Notes.notebook
Experimental Probability ­­what you got when you did this simulation (experiment).
May 24, 2016
Theoretical Probability ­­the real probability based on analyzing the outcomes mathematically
What are your chances, according to the outcomes you got, of winning $3, $1 and $0?
Find the theoretical probability of each of the outcomes:
P($3) = P($3) =
P($1) =
P($0) =
P($1) =
P($0) =
Jan 10­8:39 PM
Jan 10­8:41 PM
Find the Expected Value of this game. To find the expected value you use the theoretical probability not the experimental probability.
E(x) =
Is this game fair?
Jan 10­8:42 PM
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