Probability & Statistics 2 — A Level Mathematics 9709

Probability & Statistics 2 — A Level Mathematics 9709: 5 chapters and 301 lesson cards — AI teacher explanations, worked examples, diagrams, common mistakes and exam-style questions, aligned to the Cambridge A Level Mathematics 9709 syllabus.

Topics

  1. 6.1 The Poisson Distribution — Introduction · Key ideas — The Poisson formula · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Mean and variance · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — When is Poisson a good model? · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Poisson approximation to the binomial · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Normal approximation to the Poisson · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples · 🔍 Worked example — Easy · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  2. 6.2 Linear Combinations of Random Variables — Introduction · Key ideas — A linear function of one variable · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Combining two variables · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — 3X is not the same as X₁ + X₂ + X₃ · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Which distributions are preserved? · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Comparing two variables · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: which is bigger? · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: a total of several items · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 3: 2X versus X₁ + X₂ · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 4: sum of Poisson variables · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  3. 6.3 Continuous Random Variables — Introduction · Key ideas — The probability density function · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Finding an unknown constant · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Mean and variance · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Median and percentiles · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  4. 6.4 Sampling and Estimation — Introduction · Key ideas — Populations and samples · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — The distribution of the sample mean · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Unbiased estimates · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Confidence intervals for a mean · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Confidence intervals for a proportion · 🧑‍🏫 Teacher's explanation · 📖 Definitions · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice
  5. 6.5 Hypothesis Tests — Introduction · Key ideas — The language of testing · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Testing a binomial or Poisson observation · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Critical regions for discrete distributions · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Testing a population mean · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Key ideas — Type I and Type II errors · 🧑‍🏫 Teacher's explanation · 📖 Definitions · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · 🧠 Quick check 1 · 🧠 Quick check 2 · 🎯 Exam question · Worked examples — Example 1: binomial, one-tailed · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 2: Poisson · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 3: a mean with known σ · 🔍 Worked example — Easy · 🔍 Worked example — Exam-style · ⚠️ Common errors · Worked examples — Example 4: normal approximation · 🔍 Worked example — Easy · 🔍 Worked example — Standard · 🔍 Worked example — Exam-style · ⚠️ Common errors · Common mistakes · Practice