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Summary Further Statistics Notes

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Module
Statistics

Institution
OCR

Unlock the secrets to mastering Statistics in A Level OCR Further Maths with these comprehensive revision notes meticulously crafted to cover the entire syllabus. Condensed yet comprehensive, these notes include worked examples and explanations, providing you with a clear understanding of each conc...

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Further Statistics Complete Revision Notes

, Counting Principles & Probability:

Product Principle: n(A & B) = n(A) x n(B)
Addition Principle: n(A or B) = n(A) + n(B)

Number of arrangements of n distinct objects is n factorial; permutations means same thing
as arrangements and the number of permutations of a subset of size r from a set of n objects
is nPr

Number of ways of choosing r from n, means you use nCr

Exclusion principle: Count what you are not interested in and then subtract from total

If some of the objects have to be kept apart, permute the remaining objects and insert the
separated objects into the gaps

If there are n objects with x of A, y of B and z of C then the number of permutations = n
factorial / x factorial x y factorial x z factorial

Probability of Event A Occurring = Number of Outcomes in which A Occurs / Total Number of
Possible Outcomes

Discrete Random Variables:

Mu = E(X) = The sum of all values of x times their probabilities
Var(X) = E(X squared) - E(X) squared

If Y = aX + b then:
- E(Y) = aE(X) + b
- Var (Y) = a squared x Var(X)

Uniform Distribution, Binomial Distribution, Geometric Distribution - find all relevant formulae
in the formula book

Geometric Distribution: P(X > x) = (1 - p) power x

Poisson Distribution:

Find relevant information about E(X) and Var(X) in formula book

If X - Po (λ), Y - Po (Mu) and Z = X + Y, then Z - Po (λ + Mu)

Non Parametric Hypothesis Test:

Single Sample Sign Test: Test that allows us to decide whether the median is different from a
particular value.

H0: Median is X

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