**All of the expected value stuff is in chapter 16. If you're looking for an example to see how it's calculated, see page 369--or, of course, you can always google it!
Uncovering Expected Value
1.
The number of points obtained in one game is
independent of the number of points obtained in a second game. When the game is
played twice, the sum of the number of points for both times could be 0,1,2,3,
or 4. If Y represents the (sampling
distribution of the) sum of the two scores when the game is played twice, for
which value of Y will the probability
be the greatest?
For
one play:
P(0)
= 0.4 P(1) =
0.3 P(2) = 0.3
Find the probability for each sum to complete the probability distribution below:
|
Outcome
(Sum)
|
0
|
1
|
2
|
3
|
4
|
|
Probability
|
|
|
|
|
|
2.
Let’s turn this into a game (yes, gambling)!
Suppose we want to designate the following prize values:
$0, $100, $200, $300,
and $500
Suppose we’re a casino and designed this game (to earn
money). Which prizes should be allotted to which sums?
|
Outcome
(Sum)
|
0
|
1
|
2
|
3
|
4
|
|
Prize
|
|
|
|
|
|
|
Probability
|
|
|
|
|
|
3. Find the expected value for the
amount of the prize. Interpret this value.
4. How much money would a player
expect to earn (or lose) after 100 plays?
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