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Use a small explicit model
The fictional model has four equally probable scenarios. A return variable X maps them to −10%, 0%, 10% and 10%. The scenarios are distinct even though two have the same return.
| Outcome | Probability | X: return |
|---|---|---|
| S₁ | 25% | −10% |
| S₂ | 25% | 0% |
| S₃ | 25% | 10% |
| S₄ | 25% | 10% |
Describe the positive-return event
The event X > 0 contains S₃ and S₄. Its probability is 25% + 25% = 50%. The variable is the mapping X; the event is the set of scenarios satisfying the stated condition.
Notice that a realised value need not identify one outcome
Observing X = 10% narrows this model to S₃ or S₄ but does not distinguish between them. A description that equates every numerical value with one unique scenario would lose that distinction.
Separate a zero value from a zero probability
The outcome S₂ has a return value of 0%, but its probability is 25%. A random variable taking the value zero does not imply that the corresponding event has probability zero.