Everything else is ready: study the parts, the key terms and the quiz below.
- Part 11Which rule costs less under stated assumptions?
- Part 22Give each client an outcome and an assumed cost
- Part 33Compute the first rule's expected cost
- Part 44Compare the second rule on the same clients
- Part 55Variance describes how uneven individual costs are
- Part 66Change an assumption, not the history
- Part 77Reproduce, decide, and hand off
Random Variables, Expectation and Variance
Describe an uncertain quantity by its distribution, its average and its spread.
In this lesson7 parts
- 01Which rule costs less under stated assumptions?
- 02Give each client an outcome and an assumed cost
- 03Compute the first rule's expected cost
- 04Compare the second rule on the same clients
- 05Variance describes how uneven individual costs are
- 06Change an assumption, not the history
- 07Reproduce, decide, and hand off
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- review rule
- A declared test that assigns each row to review or no review, such as
PAY_0 > 0. - outcome cell
- One combination of assigned action and recorded label, such as a missed default.
- cost matrix
- An assumed cost for each action × outcome combination: $1,000 per missed default, $100 per reviewed nondefault, $0 otherwise.
- random variable
- A numeric value assigned to each possible outcome; here, a randomly chosen client's assigned cost.
- discrete outcome
- One of a countable set of values: $0, $100 or $1,000.
- continuous random variable
- Under a model, any value in an interval is possible, such as a review time from 0 to 10 minutes.
- uniform distribution
- Equal-length intervals have equal probability: 2 to 4 minutes has 20% under the 0–10 model.
- expected value
- The probability-weighted average of a random variable's possible values.
- long-run average (narration)
- The value a running average of repeated random draws tends toward: the expected value, by the law of large numbers.
- expected cost
- Average assigned cost under the stated outcome frequencies and cost matrix: $117.75 for
PAY_0 > 0, $97.98 forPAY_0 >= 0. - empirical variance
- The mean of squared distances from the empirical mean, in squared units.
- standard deviation
- Square root of variance, in the original units: about $306.02 for the first rule's costs.
Quiz 5 questions
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.
Practice
Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.
The self-checking notebook for this lesson is Random variables, expectation and variance.
Common mistakes
What you will see when it goes wrong, why it happens, and the fix.
Where it’s used
Where this lesson’s ideas turn up in real work.