Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can state the four conditions for a binomial random variable and explain what X counts. (Guide: “When is a random variable binomial?”)
- I can justify that a random variable is binomial by checking each condition in context. (Guide: Worked example 1; Practice Q5)
- I can explain which condition fails when a variable is not binomial, such as drawing without replacement from a small group or counting trials until a success. (Guide: Worked example 2; Practice Q1)
- I can explain what ₙCₓ counts and why the formula needs it. (Guide: “The binomial probability function”; Practice Q3)
Calculation
- I can calculate P(X = x) with the binomial probability function, showing n, p and x. (Guide: Worked example 1; Practice Q3)
- I can turn “at least”, “at most”, “more than” and “fewer than” into the right inequality and find the probability with a sum, a complement or a cdf. (Guide: Worked example 1; Practice Q4, Q5)
- I can calculate the mean np and the standard deviation √[np(1 − p)] of a binomial variable. (Guide: Worked example 3; Practice Q2, Q6)
- I can estimate a binomial probability from simulation results and compare it with the exact value. (Guide: Worked example 3; Practice Q7)
Reasoning
- I can interpret a binomial probability, the mean and the standard deviation in context. (Guide: Worked examples 1 and 3; Practice Q4, Q5)
- I can use a small binomial probability as evidence against a claim, without saying it proves anything. (Guide: Worked example 3; Practice Q6)
- I can explain why a simulation estimate differs from the exact probability and how to improve it. (Practice Q7)
All ticked? Move on to Topic 2.11, The Normal Distribution, or return to the course roadmap.