The Probability & Statistics Course Guide

Probability from zero

Events as sets, the three axioms (with a coin-toss widget), counting taught from scratch — the catch-up section — then conditioning, Bayes, and independence.

Probability

The exam-day map: counting decision table, three computed worked examples (defective sampling, three-lines Bayes, reliability), the five classic traps.

Discrete random variables from zero

Random variables, pmf and cdf, expectation as long-run average, the MGF taught from zero (it's not in Devore), then binomial (with an interactive histogram), hypergeometric, negative binomial, Poisson.

Discrete Random Variables

The exam-day map: the model-choice decision table, MGF derivations (binomial, Poisson) with the geometric-convention trap, three computed worked examples, the cdf off-by-one trap.

Continuous random variables from zero

From bars to curves: pdfs and areas, cdfs and percentiles, the normal distribution (with an interactive z-table), exponential waiting times and memorylessness.

Continuous Random Variables

The exam-day map: the discrete↔continuous dictionary, three computed worked examples (pdf workout, normal resistors, exponential lifetimes), the density-is-not-probability trap.

MGFs, Chebyshev and transformations from zero

The handout's reference-book additions to Module 3, all lectured before the mid-sem: continuous MGFs (and reading a normal straight off its MGF, as the 2025 paper demanded), limits of MGFs, Chebyshev's bound, and finding the distribution of a function of X.

MGFs, Chebyshev, Transformations

The compressed map: the continuous MGF table, recognise-the-MGF and MGF-limit worked examples from the 2025 paper, Chebyshev bound vs exact, the cdf and change-of-variable methods, classic traps, practice table.

How to start any probability problem

The four opening moves — name the events, turn every number into a P( ) statement, write the target, write its formula — shown on eight past-paper questions, openings only. The papers themselves award marks for these moves ("Define the event(s) and random variable(s) clearly"), so they're never wasted, even if you stall later.

Bayes as areas

2026 mid-sem Q6(a), acted out: a square split by the two machines, then by their defect rates. Zooming into "defective" makes P(M₂ | D) = 4/7 a share of an area you can see. It pauses three times for your next move.

Start-only drill

Fresh word problems in every past-paper family; write only the four opening moves, reveal the model opening, tick which moves you got. No arithmetic until the start is automatic. Eight openings a day.

Mid-sem past papers, from zero

The 2026 (closed book — same format as ours), 2025 and 2024 mid-sem papers, every question solved step by step with figures, the traps that cost marks, a topic × paper frequency table, a closed-book formula list and a 90-minute plan. All three papers test Modules 1–3 only.

Mid-sem PYQ drill

Fresh numbers for every question family the past papers use — normal approximation with continuity correction, exponential → binomial → Bayes, Poisson regions, hypergeometric Bayes, MGF recognition, series of games, pmf recurrence and more. Name the family, solve, check, open the method.

The quiz, question by question, from zero

The real paper (four variants, key filed): Bayes with the number of urns unknown, a conditional probability with a union in the condition (Venn drawn), and the shuffled-PINs matching problem with all 24 orders drawn and the derangement counts Devore never gives. Every variant tabulated, a twin per question, the 30-minute plan. Read before the 7 Oct mid-sem.

Doubts, worked from zero

One card per problem you send in, filed on a topic page that matches the notes (sets & addition rule · counting · conditional probability · independence & reliability · total probability & Bayes), with an index you can filter by topic, module or date. Each card: the question as set, where it lives in the notes, the explanation from first principles with the sample space drawn, the trap, and a twin. Twenty-two cards live, including six Devore worked examples (2.22, 2.26–2.29, 2.35, 2.36) explained from zero; the three Module 1 slide examples (13 Sep) and a thirteen-card batch from the Module 1 problem set (14 Sep) — Venn regions, hats, dinosaurs, phones, widgets, reliability, pairwise vs mutual, the circuit, vehicles, boxes, ball transfers, the director, two total-probability slides.

Tutorial Sheets 1–3: hints & solutions

All 27 questions from the 5, 12 and 19 Aug sheets, each mapped to its Devore section, with a method-naming hint and a collapsed verified solution. Plus what the three sheets reveal about the exam's style.

Quiz 1 questions, from zero

Last year's paper had exactly two questions, and both are standard patterns: a binomial tail feeding a Bayes flip, and E/V of a function of a random variable. Every symbol named before it's used, every arithmetic step shown, four computed figures, a slider covering all four numeric variants, the full variant table, and a 20-minute clock plan for a no-partial-credit paper.

Tutorial 2, Q5 and Q6, from zero

The two sheet questions that stack ideas: Bayes after three independent tests (the hidden likelihood built by listing sequences, then the tree and the area picture) and the birthday problem (the chain of shrinking fractions, the complement, and a slider-plus-simulation widget for the 23-people threshold). Every step unpacked, vocabulary included.

Tutorial Practice Drill

Fresh randomized problems in the nine pattern families of Tutorials 1–3 (rules, independence, sampling, trees & Bayes, tables, three-event Venns, pmfs, cdfs, expected-profit decisions). "Name the family first" — the recognition skill the sheets really test. Six per sheet, self-marking, method on every answer.

Counting Drill

Six randomized problems per sheet in Tutorial-1's exact styles — identical-item arrangements, labelled groups, the glue trick, constrained committees, sampling probability. Timed, self-marking, with a "see the method" line on every answer. Built because §2.3 is self-study.

Describing data from zero

Why engineers measure variability, populations vs. samples, histograms (with a bin-width toy to play with), centre, spread, and boxplots. No lectures cover this — it feeds the 10% R-lab component.

Overview & Descriptive Statistics

The compressed map: three computed worked examples (location, density histogram, boxplot with outliers), the n−1 trap, prerequisite kit, practice pointers. §1.5 “The same in R” covers the Lab 1 sheet function by function, corrects its summary table, and explains the moments-vs-e1071 kurtosis trap.

R lab 2 · Simulating distributions

R's d/p/q/r naming scheme with two computed figures; the three silent traps (sd not variance, rate not mean, pbinom(k − 1)); four past mid-sem answers checked in one R line each; a simulation widget where the histogram settles onto the pmf/pdf as N grows; the sheet's four wrong remarks corrected.