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
, 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
