# S2 Tutorials

## The Poisson Distribution

## Poisson Distribution

## Poisson Approximation to the Binomial Distribution

## Normal Approximation to the Poisson Distribution

## Linear combinations of random variables

## Linear combinations of random variables

- Linear combinations of discrete random variables
- E(aX + bY) = aE(X) + bE(Y)
- Var(aX + bY) = a
^{2}Var(X) + b^{2}Var(Y) for independent X and Y - If X has a normal distribution then so does aX + b
- If X and Y have independent normal distributions then aX + bY has a normal distribution
- If X and Y have independent Poisson distributions then X + Y has a Poisson 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)
- Exam Questions - Probability density functions and cumulative distribution functions

## Estimation and Sampling

## Estimation and Sampling

- Difference between between a sample and a population
- Random sampling using random number tables or calculator
- Simple random sampling
- What is a statistic?
- Sampling distribution of the sample mean
- Sampling distribution of the mode and median
- Exam Questions - Estimation and sampling, Median
- Central limit theorem
- Unbiased estimates of the population mean and variance from a sample
- Confidence interval for a population mean
- Confidence interval for a population proportion
- Exam Questions - Estimation and sampling, Range