AQA Further Statistics A-Level Tutorials

Discrete Probability Distributions

1. Probability distribution tables
2. Expected values E(X)
3. Expected values E(X²)
4. Variance, Var(X)
5. Median from a discrete probability distribution
6. Mode from a discrete probability distribution
7. Linear combinations of discrete random variables
8. Exam Questions - Discrete random variables
9. Expected value and variance of a function of X

Uniform Distribution (Rectangular Distribution)

1. Discrete uniform 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

Hypothesis Tests – Poisson Distribution

1. Test for a Poisson mean
2. Lower tail test
3. Upper tail test
4. Two tailed test
5. Exam Questions - Hypothesis tests: Poisson distribution
6. Hypothesis test for the population mean

1. What are Type I and Type II errors?
2. Type I error for a Binomial distribution
3. Type 1 error for a Poisson distribution
4. Type I error for a Normal distribution
5. The power of a test

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. Exam Questions - Probability density functions and cumulative distribution functions

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

The Chi-Squared test

1. Chi squared test for contingency tables
2. Yates continuity correction

1. Exponential distribution

The t-distribution

1. t-distribution

Confidence intervals

1. Confidence intervals for the mean of a normal population
2. t-tests for confidence intervals