Maths — Statistics 2

Maths YMA01 — specification explorer

All 16 specification statements from the official Pearson Edexcel specification, as printed — filter by paper, unit or tier exactly as Pearson Edexcel assesses them.

Scope the specification

16 spec points

Unit

Every statement · S2

Assessment homes come from the parsed Pearson specification (content summaries & assessment overviews). Hover a chip for the printed rule. Filters appear only where the qualification has that structure — a linear IGCSE has no unit scope, and only Maths A splits Foundation / Higher tiers.

1. The Binomial and Poisson distributions

1.1
The binomial and Poisson distributions.:
- Students will be expected to use these distributions to model a real-world situation and to comment critically on their appropriateness. Cumulative probabilities by calculation or by reference to tables. Students will be expected to use the additive property of the Poisson distribution – e.g. if the number of events per minute ∼ Po(λ) then the number of events per 5 minutes ∼ Po(5λ).
S2
1.2The mean and variance of the binomial and Poisson distributions. No derivations will be required.S2
1.3The use of the Poisson distribution as an approximation to the binomial distribution.S2

2. Continuous random variables

1. Continuous random variables

2.1The concept of a continuous random variable.S2
2.2The probability density function Use of the probability density function f( x ), where and the cumulative distribution b function for a continuous random P( a < X ≤ b ) = f ( x ) d x . variable. ∫ a Use of the cumulative distribution function x 0 F( x 0 ) = P( X ≤ x 0 ) = f ( x ) d x . ∫ −∞ The formulae used in defining f( x ) will be restricted to simple polynomials which may be expressed piecewise.S2
2.3
Relationship between density and distribution functions.:
- dF(x) f(x) = . dx
S2
2.4Mean and variance of continuous random variables.S2
2.5Mode, median and quartiles of continuous random variables.S2

3. Continuous distributions

1. Continuous distributions

3.1The continuous uniform (rectangular) distribution. Including the derivation of the mean, variance and cumulative distribution function.S2
3.2Use of the Normal distribution as an approximation to the binomial distribution and the Poisson distribution, with the application of the continuity correction.S2

4. Hypothesis tests

1. Hypothesis tests

4.1Population, census and sample. Sampling unit, sampling frame. Students will be expected to know the advantages and disadvantages associated with a census and a sample survey.S2
4.2Concepts of a statistic and its sampling distribution.S2
4.3Concept and interpretation of a hypothesis test. Null and alternative hypotheses. Use of hypothesis tests for refinement of mathematical models.S2
4.4Critical region. Use of a statistic as a test statistic.S2
4.5One-tailed and two-tailed tests.S2
4.6
Hypothesis tests for the parameter p of a binomial distribution and for the mean of a Poisson distribution.:
- Students are expected to know how to use tables to carry out these tests. Questions may also be set not involving tabular values. Tests for the parameter p of a binomial distribution may involve the use of a normal approximation to calculate probabilities.
S2