# OCR Further Maths Statistics A-Level

It is advisable to check the official OCR Further Maths Statistics A-Level specification in case of any changes.

## Probability using Permutations and Combinations

- Permutations of n different items
- Permutations of r items from n different items
- Permutations of repeated letters in a word
- Permutations with restrictions: letters / items together
- Permutations with restrictions : items at the ends
- Permutations with restrictions : items must not be together
- Combinations of n different items
- Combining combinations
- Probability using permutations and combinations

## Discrete Random Variables

## Binomial Distribution

## Geometric Distribution

## Poisson Distribution

## Uniform Distribution (Rectangular Distribution)

## Continuous Random Variables

## Probability Density Functions and Cumulative Distribution Functions

- What is a probability density function (p.d.f.)?
- Finding the constant k in a p.d.f
- Calculating probability from a p.d.f.
- The cumulative distribution function, (c.d.f)
- Finding the median quartiles and percentiles
- Finding the mode from a p.d.f.
- E(X) and Var(X)
- E[g(x)]
- Exam Questions - Probability density functions and cumulative distribution functions
- Related Random Variables

## Continuous Uniform / Rectangular Distribution

## Linear Combinations of Random Variables

## The Normal Distribution

- The normal distribution
- Normal Cumulative Distribution Function
- Inverse Normal Function to find observed values
- The standard normal distribution Z~N(0,1) - Using tables or calculator
- Probabilities from a normal distribution using tables
- Exam Questions - Normal distribution, finding a probability
- Calculating the mean μ and standard deviation σ
- Exam Questions - Calculating the mean and standard deviation
- Exam Questions - Finding an observed value
- The Sums and Differences of Normal Variables
- Linear Combinations of Normal Random Variables
- More than two independent normal random variables
- Sampling distribution of the sample means (Normal distribution)
- Sampling distribution of the sample means (Normal distribution) proof
- Introduction to Hypothesis testing for Normal distribution
- Hypothesis testing for Normal distribution (One tailed and 2 tailed test)
- Understanding Critical values (Hypothesis testing for Normal Distribution)
- Hypothesis testing for Normal Distribution - Critical values method (3 examples)

## The Distribution of the Sample Mean

## Chi Squared Tests

- Chi squared test for contingency tables
- Yates continuity correction
- Chi-squared test for goodness of fit for a Binomial Distribution
- Chi-squared test for goodness of fit for a Poisson distribution
- Chi-squared test for goodness of fit for a Discrete Uniform distribution
- Chi-squared test for goodness of fit for a Geometric distribution
- Chi-squared test for goodness of fit for a Normal distribution