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 explain what a parameter is and why it has one fixed value. (Guide: “Parameters and statistics”; Practice Q2)
- I can tell a parameter (μ, σ) from a statistic (x̄, s) in a given situation. (Guide: simulation section; Practice Q2, Q7)
- I can explain why the expected value need not be a possible value of X, and why it is not the most likely value. (Guide: “The mean (expected value)”; Practice Q1, Q3)
- I can explain why the standard deviation of a random variable has no n − 1 in it. (Guide: FAQ and misconceptions)
Skills
- I can check that a table is a valid probability distribution and find a missing probability. (Practice Q5)
- I can calculate the expected value of a discrete random variable as a weighted sum. (Guide: Worked example 1; Practice Q1, Q4)
- I can calculate the variance and standard deviation of a discrete random variable, showing the deviations, squares and weights. (Guide: Worked examples 1 and 2; Practice Q4, Q6)
- I can check my answers with one-variable statistics, using the probabilities as frequencies and reading σx. (Guide: Worked example 1)
Reasoning
- I can interpret the mean as a long-run average, in context with units. (Guide: Worked example 2; Practice Q3, Q5)
- I can interpret the standard deviation as a typical long-run distance from the mean, in context. (Practice Q4)
- I can use the mean to estimate a long-run total, such as income over many plays. (Guide: Worked example 2; Practice Q5)
- I can compare two random variables with the same mean by their standard deviations to support a decision. (Practice Q6)
All ticked? Move on to Topic 2.10, The Binomial Distribution, or return to the course roadmap.