Expected value
| 0 | 0.1 | 0 |
| 1 | 0.3 | 0.3 |
| 2 | 0.4 | 0.8 |
| 3 | 0.2 | 0.6 |
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Long-run average, not one result: E(X) = 1.7 means the average approaches 1.7 over many tries.
One try still gives a whole score: 0, 1, 2 or 3.
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Expected value on the GDC
A game has the probability distribution below. Calculate the expected score E(X) using your GDC. [2]
| x | 0 | 2 | 5 | 20 |
|---|---|---|---|---|
| P(X = x) | 0.5 | 0.3 | 0.15 | 0.05 |
GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
Show your method: For a simple table, also know how to write the expected-value substitution by hand.
For the GDC example: E(X) = 0(0.5) + 2(0.3) + 5(0.15) + 20(0.05) = 2.35.
Separate question: find the unknown value
X has the probability distribution below. Given that E(X) = 1, find n. [3]
| x | −2 | 1 | n |
|---|---|---|---|
| P(X = x) | 0.4 | 0.45 | 0.15 |
Given E(X) = 1, find n.
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Exam-style question
Try it, then check
A score is 0, 2 or 5 with probabilities 0.5, 0.3 and 0.2. Find E(X) and explain its meaning. [3]
Step by step
- Multiply each score by its chance, then add.
Final answer
Over many plays, the average score approaches 1.6. One play gives 0, 2 or 5, never 1.6.