Connect the ideas.
- A discrete variable has listable numerical outcomes; a valid mass function has non-negative entries summing to 1.
- Cumulative probability includes its endpoint: F(x) = P(X ≤ x). Translate strict inequalities before using a cumulative calculation.
- E(X) is a probability-weighted long-run mean, not a guaranteed or necessarily possible outcome.
- Variance is E(X²) − [E(X)]²; SD is its non-negative square root in the original units.
- For aX + b, the mean changes by aμ + b and variance by a²v; a fixed shift does not change spread.
- Means add without independence. Adding variances with squared coefficients requires the independence assumption used here.
- Binomial counts require fixed n, two trial categories, independent trials and common p; use np and np(1 − p) for their summaries.
- State assumptions, units and event endpoints, retain calculator precision until the last step, and interpret decisions in context.
Put it together.
Choose a paper and show your working.
Discrete distributions — Practice test 1
Build confidence with tables, cumulative probabilities, summary measures and an ordinary binomial model.
10 questions · 58 marks · 70 minutes · Technology-assistedDiscrete distributions — Practice test 2
Compare models, recover a distribution from cumulative information and examine the role of independence.
10 questions · 64 marks · 70 minutes · Technology-assistedDiscrete distributions — Practice test 3
Apply the models to service times, insurance, tariffs and capacity decisions, with explicit assumptions.
10 questions · 62 marks · 70 minutes · Technology-assistedDiscrete distributions — Practice test 4
Explain distribution identities, distinguish dependent indicators and solve a minimum-trial problem.
10 questions · 64 marks · 70 minutes · Technology-assistedDiscrete distributions — Practice test 5
Connect cumulative thresholds, nonlinear transformations, costs and repeated sampling without losing the model assumptions.
10 questions · 65 marks · 75 minutes · Technology-assistedDiscrete distributions — Applications and reasoning test
An integrated paper requiring distribution construction, nonlinear costs, model criticism and justified decisions.
10 questions · 72 marks · 75 minutes · Technology-assisted
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 Mathematical Methods: discrete random variables and probability distributions, expected value and variance, transformations and independent sums, Bernoulli and binomial models. Original supporting lessons and exercises follow the approved Ascent chapter structure.
Official curriculum source ↗