OCR Further Maths Statistics A-Level

1. Permutations of n different items
2. Permutations of r items from n different items
3. Permutations of repeated letters in a word
4. Permutations with restrictions: letters / items together
5. Permutations with restrictions : items at the ends
6. Permutations with restrictions : items must not be together
7. Combinations of n different items
8. Combining combinations
9. Probability using permutations and combinations

1. Probability distribution tables
2. Expected values E(X)
3. Expected values E(X²)
4. Variance, Var(X)
5. Linear combinations of discrete random variables
6. E(aX + bY) = aE(X) + bE(Y)
7. Var(aX + bY) = a²Var(X) + b²Var(Y)
8. Exam Questions - Discrete random variables

Binomial Distribution

1. Binomial distribution
2. Binomial probabilities on a calculator
3. Cumulative probability tables
4. Mean and variance
5. Exam Questions - Binomial distribution

Geometric Distribution

1. Geometric distribution
2. Calculating probabilities
3. Calculating least trials before a success
4. The expected value, E(X)
5. The variance Var(X) - Geometric Distribution

Poisson Distribution

1. Poisson distribution
2. Changing the mean
3. Finding an observed value x
4. Sum of two Poisson distributions
5. Exam Questions - Poisson distribution

Uniform Distribution (Rectangular Distribution)

1. Discrete uniform distribution

Probability Density Functions and Cumulative Distribution Functions

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

Continuous Uniform / Rectangular Distribution

1. Continuous uniform / rectangular distribution
2. Defining the pdf, calculating probabilities and quartiles
3. Expected mean E(X), the variance Var(X), cumulative distribution function F(X)
4. Exam Questions - Continuous uniform / rectangular distribution

1. Combining means and variances from distributions

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

The Distribution of the Sample Mean

1. The distribution of the sample mean
2. Central Limit Theorem

1. Unbiased estimator for the population mean
2. Unbiased estimator for the population variance

Testing a population mean based on a sample mean

1. Sample drawn from a normal distribution with known population variance
2. Large sample drawn from any population with known variance
3. Large sample drawn from any population with unknown variance

1. Sample taken from a normal distribution with known population variance
2. Large sample taken from any population with known variance
3. Large sample taken from any population with unknown variance

1. Chi squared test for contingency tables
2. Yates continuity correction
3. Chi-squared test for goodness of fit for a Binomial Distribution
4. Chi-squared test for goodness of fit for a Poisson distribution
5. Chi-squared test for goodness of fit for a Discrete Uniform distribution
6. Chi-squared test for goodness of fit for a Geometric distribution
7. Chi-squared test for goodness of fit for a Normal distribution

1. What is a non-parametric test?

The Sign Test

1. The sign test

Wilcoxon sum rank test

1. The Wilcoxon sum rank test

Wilcoxon signed rank test

1. The Wilcoxon signed rank test

Correlation

1. Correlation
2. Product moment correlation coefficient (pmcc)
3. Measuring linear correlation using a calculator
4. Exam Questions - Correlation
5. Hypothesis testing for zero correlation

Regression

1. Regression
2. Interpreting the regression line constants, explanatory and response variables
3. Making predictions and reliability of predicted values
4. Exam Questions - Regression

Spearman’s Rank Correlation Coefficient

1. Spearman's rank correlation coefficient
2. Exam Questions - Spearman's Rank Correlation Coefficient
3. Hypothesis testing for Spearman's correlation coefficient