Confidence Intervals (1) |
Confidence limits. Mean and difference of means of normal distributions with known variances. |

Confidence Intervals (2) |
Further confidence limits for unknown means when variances are unknown. Large sample approximations. |

Continuous Distributions |
Continuous probability functions. Calculation of the mean and variance and use of expectation function. Particular applications to the uniform and normal distributions. Sum of n independent random variables is approximately normal. |

Descriptive Statistics |
Graphical ways of presenting data and methods for summarising the derived distributions. |

Discrete Distributions |
Discrete probability functions. Calculation of the mean and variance and use of the expectation function. Particular applications to the Binomial and Poisson distributions. Poisson approximation to the binomial. |

Distribution of Sample Means |
Properties of random samples. Distribution of the sample mean and use of the Central Limit Theorem. |

Estimation |
Estimation of population parameters. Unbiased estimators and variance criterion to choose best estimator. |

Hypothesis Testing (1) |
Hypothesis testing, significance levels and p values. Tests for the mean of a Binomial, Poisson or normal distribution. Difference of normal means with known variances. |

Hypothesis Testing (2) |
Further hypothesis testing for means and difference of means when the variances are unknown. Large sample approximations. |

Probability |
Random experiments, sample spaces and rules of probability. Conditional probability, Law of Total Probability and Bayes’ Theorem. |

Regression |
Least squares methodology for fitting a straight line. Hypothesis test and confidence limits for estimated parameters of specified regression models. |