Section 8.2 – Expected Value
1
Section 8.2
Expected Value
The
average
(mean) of
n
numbers,
x
1
, x
2
, x
3
,…, x
n
is
x
.
n
x
x
x
x
n
+
+
+
=
...
2
1
Expected Value of a Random Variable
X
Let
X
denote a random variable that assumes the values
x
1
, x
2
, x
3
,…, x
n
with associated
probabilities
p
1
p
2
, …, p
n
,
respectively.
The
expected value
of
X
,
E
(
X
), is given by
n
n
p
x
p
x
p
x
X
E
+
+
+
=
...
)
(
2
2
1
1
Example 1:
In this Finite Math class each of the 4 tests are worth 12%, the quiz average
is worth 12%, the homework average is worth 8%, the popper average is worth 8%, and
the final exam is worth 24%.
If your grades are as follows:
Test 1 – 82, Test 2 – 76, Test 3 – 87, Test 4 – 90, Quiz Average – 100, Homework
Average – 91, Popper Average – 100, and Final Exam – 95.
What is your class average (expected value)?
Example 2:
A box contains 15 quarters, 7 dimes, 5 nickels, and 8 pennies.
A coin is
drawn at random from the box.
What is the mean of the value of the draw?