Chapter 12 — Probability and statistics
Lesson map
Lesson 12 published. Map, example, EX034.
flowchart TD
N0["Learning outcomes"]
N1["12.1 Describing data"]
N2["12.2 Reasoning with probability"]
N3["12.3 Common mistakes"]
N4["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4
N4 --> EX["Worked example"]
EX --> Q["Exercise EX034"]
Logical drawing
flowchart LR
N0["Learning outcomes"]
N1["12.1 Describing data"]
N2["12.2 Reasoning with probability"]
N3["12.3 Common mistakes"]
N4["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4 --> Q["EX034"]
[Learning outcomes]
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v
[12.1 Describing data]
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v
[12.2 Reasoning with probability]
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v
[12.3 Common mistakes]
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v
[Synthesis]
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v
[Worked example] --> [Exercise EX034]
Learning outcomes
You will (1) describe data with summaries; (2) reason with probability; (3) avoid common statistical mistakes.
12.1 Describing data
Sofia receives a synthetic year of weekly voucher issuance. She computes the mean, median and spread, and plots a histogram. Issuance is usually between 4,000 and 7,000 vouchers a week, with a holiday dip and a harvest-season peak. The median is less affected by a few unusual weeks than the mean. Summaries tell her what normal looks like, which is the basis for spotting abnormal behaviour later. She labels every chart with its source, period and units, so that a board member reading it months later can understand exactly what it shows and where the numbers came from.
12.2 Reasoning with probability
Probability describes uncertainty. Sofia studies Nakamoto's calculation of the chance that a minority of computing power could catch up with the honest chain after a number of confirmations, which falls quickly as confirmations increase. On the cooperative's permissioned ledger, finality works differently, but the idea of waiting for evidence before trusting a result carries over. She also estimates simple probabilities from data: if two of 52 weeks had a reconciliation mismatch, a rough weekly rate is about 4 percent. She notes that small samples give uncertain estimates, so she reports the counts behind every percentage she writes.
12.3 Common mistakes
Sofia lists mistakes she must avoid. Correlation is not causation: weeks with more vouchers are also weeks with more shop sales, but neither causes the other; both follow the harvest. Small samples mislead: two incidents in a year say little about next year. Base rates matter: an alert that fires on 1 percent of normal weeks will produce many false alarms if real problems are rare. She writes each mistake beside an example from the cooperative's data. Dr Asante says that honest statistics are part of security reporting, because exaggerated numbers lead to wasted effort or misplaced reassurance.
Worked example
Sofia summarises weekly issuance with medians, estimates a mismatch rate of about 4 percent from 2 of 52 weeks and reports the counts.
Synthetic case. Issuance data are synthetic; Nakamoto (2008) is a real source.
Errors and limits
Reporting a percentage without its counts hides how uncertain a small-sample estimate is.
Exercises
- EX034 — Normal range. What is normal weekly issuance? Rubric: 3 = between 4,000 and 7,000;; 2 = 4,000–7,000;; 1 = 18,000;; 0 = none.
- EX035 — Mismatch estimate. What rough weekly mismatch rate does she estimate? Rubric: 3 = about 4 percent from 2 of 52;; 2 = 4 percent;; 1 = 50 percent;; 0 = none.
- EX036 — Base-rate warning. Why do base rates matter for alerts? Rubric: 3 = rare problems mean many alerts are false alarms;; 2 = false alarms;; 1 = they do not;; 0 = none.
Synthesis
Honest summaries and probability reasoning give security reports a sound base.
Continue studying — chapter 12 of 40
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