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AP Statistics: Random Variable Examples WKS #1
Example 1:
Date___________________________
Flip 4 coins.
Let random variable X = the number of heads.
Value of X
Probability
Find:
1)
P(X = 3) =
2)
P(X  2) =
3)
P(X  2) =
4)
P(1  X  4) =
5)
P(X  1.5)
6)
Expected value (or mean) of X.
7)
Standard Deviation of X.
=
0
1
2
3
4
Example 2:
At a carnival, a game of chance involves spinning a wheel that is divided into 60 equal
sectors. The sectors are marked as follows:
$20
$10
$5
No Prize
-
1 sector
2 sectors
3 sectors
54 sectors
The carnival owner wants to know the average expected payout (from the owner’s perspective) for this game
and the amount of variability (as measured by the standard deviation) associated with it. Make sure to create
a probability distribution table first.
Example 3: Refer to the carnival game in the previous example. Suppose the cost to play the game is $1.
What are the player’s expected winnings?
Example 4: A player pays you $5 and draws a card from a deck. If he draws the ace of hearts, you pay him
$100. For any other ace, you pay $10, and for any other heart, you pay $5. If he draws anything else, he loses.
Create a probability distribution table that shows the payoff from your perspective. What is the expected
payoff? Then find the variance.