# Statistics 2 ST104b

## Half course

This half course requires the student to develop the concepts introduced in ST104a Statistics 1 of measurement and hypothesis testing.

### Prerequisites/ Exclusions

This course must be taken at the same time as or after:

• ST104a Statistics 1.

### Topics covered

Probability:

• Set theory: the basics
• Axiomatic definition of probability
• Classical probability and counting rules
• Conditional probability and Bayes’ theorem.

Random variables:

• Discrete random variables
• Continuous random variables.

Common distributions of random variables:

• Common discrete distributions
• Common continuous distributions.

Multivariate random variables:

• Joint probability functions
• Conditional distributions
• Covariance and correlation
• Independent random variables
• Sums and products of random variables.

Sampling distributions of statistics:

• Random samples
• Statistics and their sampling distributions
• Sampling distribution of a statistic
• Sample mean from a normal population
• The central limit theorem
• Some common sampling distributions
• Prelude to statistical inference.

Point estimation:

• Estimation criteria: bias, variance and mean squared error
• Method of moments estimation
• Least squares estimation
• Maximum likelihood estimation.

Interval estimation:

• Interval estimation for means of normal distributions
• Use of the chi-squared distribution
• Confidence intervals for normal variances.

Hypothesis testing:

• Setting p-value, significance level, test statistic
• t tests
• General approach to statistical tests
• Two type of error
• Tests for normal variances
• Comparing two normal means with paired observations
• Comparing two normal means
• Tests for correlation coefficients
• Tests for the ratio of two normal variances

Analysis of variance:

• One-way analysis of variance
• Two-way analysis of variance.

Linear regression:

• Simple linear regression
• Inference for parameters in normal regression models; Regression ANOVA; Confidence intervals for E(y); Prediction intervals for y; Multiple linear regression models.

### Learning outcomes

If you complete the course successfully, you should be able to:

• Apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments
• Explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform tests in a number of different settings
• Demonstrate understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems.

### Assessment

Unseen written examination (2 hr).