Discrete probability distributions — Topic Review | Year 12

QUICK RECAP

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.

Complete each paper and show your working.

Discrete distributions — Practice test 1
10 questions · 58 marks · 70 minutes · Technology-assisted
Build confidence with tables, cumulative probabilities, summary measures and an ordinary binomial model.
Open test Marking guide
Discrete distributions — Practice test 2
10 questions · 64 marks · 70 minutes · Technology-assisted
Compare models, recover a distribution from cumulative information and examine the role of independence.
Open test Marking guide
Discrete distributions — Practice test 3
10 questions · 62 marks · 70 minutes · Technology-assisted
Apply the models to service times, insurance, tariffs and capacity decisions, with explicit assumptions.
Open test Marking guide
Discrete distributions — Practice test 4
10 questions · 64 marks · 70 minutes · Technology-assisted
Explain distribution identities, distinguish dependent indicators and solve a minimum-trial problem.
Open test Marking guide
Discrete distributions — Practice test 5
10 questions · 65 marks · 75 minutes · Technology-assisted
Connect cumulative thresholds, nonlinear transformations, costs and repeated sampling without losing the model assumptions.
Open test Marking guide
Discrete distributions — Applications and reasoning test
10 questions · 72 marks · 75 minutes · Technology-assisted
An integrated paper requiring distribution construction, nonlinear costs, model criticism and justified decisions.
Open test Marking guide