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Expected Value
Expected Value
Simple Example
■ A biased die has the probability of landing on a 6 of 0.5. All
other numbers have an equal probability of appearing.
■ The die rolled 150 times. How many 6’s would you expect to
see?
0.5 x 150 = 75
■ How many 2’s would you expect?
P(2) = 0.1
Expected value = 0.1 x 150 = 15
Expected Value
Example
■ Machines break down 0, 1, 2, 3, or 4 times per month.
■ Relative frequency of breakdowns , or a probability
distribution:
Random Variable x
(Number of Breakdowns)
0
1
2
3
4
P(x)
.10
.20
.30
.25
.15
1.00
■ What is the expected number of breakdowns per month?
Expected Value
Example
■ The expected value of a random variable is calculated by finding
the expected value of each individual event and adding them.
Random Variable x
(Number of Breakdowns)
0
1
2
3
4
P(x)
.10
.20
.30
.25
.15
1.00
■ Expected value of number of breakdowns per month:
E(x) = (0)x(.10) + (1)x(.20) + (2)x(.30) + (3)x(.25) + (4)x(.15)
= 0 + 0.20 + 0.60 + 0.75 + 0.60
= 2.15 breakdowns