Expected Value
See how to find the expected value of an event.
2 examples and their solutions.
Expected Value
Formula
E(X) = x1p1 + x2p2 + x3p3 + ...
xi: Result value of an event i xi: Probability of an event i
p1 + p2 + p3 + ... = 1
Example
A coin is tossed once.
If you get a head, you get 2 points.
If you get a tail, you lose 1 point.
Find the expected value of the points.
Solution If you get a head, you get 2 points.
If you get a tail, you lose 1 point.
Find the expected value of the points.
1) Head
x1 = 2
p1 = 12 - [1]
2) Tail
x1 = -1
p2 = 12 - [2]
E(X) = 2⋅12 + -1⋅12
= 1 - 12
= 12 - [3]
x1 = 2
p1 = 12 - [1]
2) Tail
x1 = -1
p2 = 12 - [2]
E(X) = 2⋅12 + -1⋅12
= 1 - 12
= 12 - [3]
[1]
Probability of getting a head
[2]
Probability of getting a tail
[3]
This means if you toss a coin once,
you expect to get 1/2 points.
you expect to get 1/2 points.
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Example
For the given spinner,
if you spin the arrow once,
find the expected value of the points.
Solution if you spin the arrow once,
find the expected value of the points.
E(X) = 1⋅38 + 2⋅38 + 3⋅28
= 3 + 6 + 68
= 9 + 68
= 158
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