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 random variable is, and the difference between X and x. (Guide: “What is a random variable?”)
- I can tell a discrete random variable from a continuous one, with an example of each. (Guide: “What is a random variable?”)
- I can state the two rules for a valid probability distribution. (Guide: “The probability distribution of a discrete random variable”; Practice Q1)
- I can explain why the values of X need not be equally likely, even when the outcomes are. (Guide: Worked example 3; Practice Q7(a))
Skills
- I can construct a probability distribution by listing outcomes and adding the probabilities that give each value of X. (Guide: Worked example 1; Practice Q4, Q7(b))
- I can find an unknown constant in a distribution given as a function. (Guide: Worked example 2; Practice Q5)
- I can show a distribution as a table and as a probability histogram. (Guide: Figure 1)
- I can build a cumulative distribution and use it to find single probabilities by subtraction. (Guide: Worked example 2; Practice Q3, Q5)
- I can translate “at most”, “fewer than”, “at least” and “more than” into the correct inequality. (Guide: “The cumulative distribution”; Practice Q2)
- I can estimate a distribution from the results of a simulation using relative frequencies. (Guide: Worked example 3; Practice Q6)
Reasoning
- I can describe a simulation that matches a random process, and justify the random-number rule. (Guide: Worked example 3; Practice Q6(a))
- I can compare a simulated distribution with the exact one and explain why they differ. (Practice Q6(c), (d))
All ticked? Move on to Topic 2.9, Parameters of Random Variables, or return to the course roadmap.