Expectancy and outcome distributions

EN source master · P06-L03 · 30 minutes estimated · needs_review

Offline formative study. No wallet connection, real funds, private keys, signatures, live trade or personal portfolio inputs. Visuals are specifications. This source master remains needs_review; completing the formative exercise does not issue certification.

A positive mean in a tiny sample can hide severe outcomes and selection bias.

Define the outcome unit

One R is the original fixture's planned movement-loss unit. An outcome of−4R is possible because a plan is not a realized-loss cap. Keep gross and net outcomes distinct. With proportions p and 1−p and fixed payoff magnitudes, modeled mean=p×gain−(1−p)×loss; variable outcomes require averaging actual values.

Do the sample calculation

The five gross observations [2,2,−1,−1,−1] sum to 1R, so mean 0.2R. A stipulated0.1R cost per observation gives net mean 0.1R. Four out of five profitable outcomes are not implied; observed win proportion is 2/5.

Test distribution sensitivity

Add a sixth gross outcome−4R. The sum becomes−3R, mean−0.5R; net mean−0.6R if the same0.1R cost applies. This one stipulated tail event reverses the sign. Do not replace its magnitude with the planned−1R merely to preserve the attractive result.

Scope statistical uncertainty

NIST describes how sample-mean uncertainty depends on sample size, dispersion and assumptions [NIST]. These selected fictional outcomes do not establish independent identically distributed draws, a stable population or a future edge. A formal confidence interval would need a justified sampling model; this lesson calculates no such interval. Journal all outcomes, costs, omissions and regime labels; leave future probabilities UNKNOWN.

• R: stated fixture's planned loss unit.
• Empirical expectancy: sample average outcome.
• Net outcome: gross less stated costs.
• Tail sensitivity: effect of unusually large outcomes.

ILLUSTRATIVE outcomes S1–S5=[+2,+2,−1,−1,−1]R; cost 0.1R each. Stress extension S6=−4R, same cost. The samples are original teaching inputs, not claimed historical results.

Outcome-distribution bars with individual magnitudes, gross/net mean lines and separate sixth-event sensitivity lane; holder-distribution catalog family adapted to outcome counts with no wallet/holder implication.

The original samples' gross/net means and sensitivity to a stipulated larger loss.

A strategy win probability, independent draws, stable distribution or future profitable expectancy.

• OBSERVED: FIX-P06-L03 lists two+2R and three−1R outcomes.
• INFERRED: five-outcome net mean 0.1R using stated cost.
• UNKNOWN: future outcome probabilities.
• INSUFFICIENT EVIDENCE: the sample establishes a durable positive edge.

• Using win rate without payoff magnitudes.
• Ignoring costs.
• Discarding a gap loss as outside the plan.

Compute five-event win proportion, gross/net mean and total net outcome. Repeat after S6. Explain one selection-bias risk and one missing assumption for a future expectancy claim.

Deliver calculations or annotations, claim/source table and limitations. Suggested allocation: study 12 minutes, exercise 8, correction/quiz 10; estimate subject to calibration.

• Include every supplied outcome.
• Keep payoff, count and costs distinct.
• Test tail sensitivity.
• Avoid future probability claims.

Empirical expectancy is arithmetic on a stated sample; costs, tails and sampling assumptions limit any broader interpretation.

• Calculate empirical mean outcomes with costs.
• Separate sample expectancy from future distribution.

P06-L04 after correction review.

NONE in the authoritative catalog. The supplied offline fixture/package is sufficient; no paid feature or unverified Production capability is required. Lab/certification metadata denotes downstream associations, not access gates or live awards.

• [NIST] NIST — Confidence limits for mean — Sample-mean uncertainty depends on dispersion, size and assumptions. Checked 2026-10-01; locator turn11view4.