Statistical distributions (AS Unit 2: Applied Mathematics A) — WJEC A-Level Mathematics
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Statistical distributions (AS Unit 2: Applied Mathematics A) explained
A discrete random variable X takes countable numerical outcomes with specified probabilities, defined via a table or formula P(X = x).
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Two foundational axioms must be satisfied: 0 ≤ P(X = x) ≤ 1 for every outcome x, and Σ P(X = x) = 1 across the support. In problems, distributions are often given in terms of an unknown constant k (e.g. P(X = x) = kx for x = 1, 2, 3, 4). Candidates sum the algebraic expressions over all possible values of x, equate the total to 1, solve for k, and evaluate probabilities for composite events such as P(X > 2) or P(1 ≤ X < 4).
Your focus
- Represent and interpret discrete probability distributions using tables and formulas.
- Determine unknown parameters in discrete distributions using the condition that total probability equals 1.
- Calculate probabilities for compound events by summing individual probability mass terms.
Statistical distributions (AS Unit 2: Applied Mathematics A) exam tips
Marking Points
- setting up the total probability equation Σ P(X = x) = 1 across all outcomes
- solving the linear equation to find the exact value of the unknown parameter k
- evaluating the probability of a compound event by summing relevant individual probabilities
Examiner Tips
- 💡Show the full sum of probabilities equal to 1 clearly before solving for the unknown constant.
- 💡List the discrete integer values satisfying an inequality before summing their respective probabilities.
Common Mistakes
- omitting outcomes when setting the sum of probabilities equal to 1
- misinterpreting discrete inequalities, such as including x = 2 when evaluating P(X > 2)