Expected Value practice problems

Recognition audit

Signals that this is the right method

1. The question asks for a mean, average payment, premium, expected count, or long-run cost.
2. A transformed quantity g(X), rather than X itself, is the actual outcome whose average is required.
3. Several groups or stages suggest conditioning first and then averaging conditional expectations.
4. A nonnegative variable is described through its survival function, making a tail integral convenient.

Before calculation

A disciplined first pass

Name the requested quantity, mark its units or time point, and identify the assumption that permits the formula. Only then insert the numerical inputs. This separates model errors from arithmetic errors and makes the answer-choice comparison auditable.

LOTUS

Use the sum or integral over the support of X; a transformed density is not required.

Linearity

Linearity does not require independence.

Tail integral

For a limited value, truncate the upper limit at the policy limit or cap.