1. Use software R to display and analyse data, perform tests and demonstrate basic statistical concepts.

2. Describe statistical data and display it using variety of plots and diagrams.

3. Understand basic laws of probability: law of total probability, independence, Bayes’ rule.

4. Be able to estimate mean and variance.

5. Be familiar with properties of some probability distributions and relations between them: Binomial, Poisson, Normal, t, Chi-squared.

6. To perform simple statistical tests: goodness-of-fit test, z-test, t-test.

7. To understand and be able to interpret p-values.

8. To be able to report finding of statistical outcomes to non-specialist audience.

9. Group work will help students to develop transferable skills such as communication, the ability to coordinate and prioritise tasks, time management and teamwork.

(LO1) An ability to apply statistical concepts and methods covered in the module's syllabus to well defined contexts and interpret results.

(LO2) An ability to understand, communicate, and solve straightforward problems related to the theory and derivation of statistical methods covered in the module's syllabus.

(LO3) An ability to understand, communicate, and solve straightforward theoretical and applied problems related to probability theory covered in the syllabus.

(LO4) Use the R programming language fluently in well-defined contexts. Students should be able to understand and correct given code; select appropriate code to solve given problems; select appropriate packages to solve given problems; and independently write small amounts of code.

Introduction and description of data: graphical summaries, shape, location and spread of data.

Elements of Probability Theory:
• intuitive meaning of probability
• events and compound events
• conditional probability and Bayes' rule
• independence

Discrete and continuous random variables:
• probability mass function, probability density function and distribution function
• generating random variables
• expectation, variance and covariance
• Binomial and Poisson distributions
• Normal distribution, t-distribution
• approximations
• Central Limit Theorem

Statistical Inference:
• principles of hypothesis testing and interpretation of p-values; type I and type II errors
• Chi-squared test of goodness of fit and chi-squared test of association
• distrib ution of sample mean and sample variance
• Normal confidence intervals and z-test for mean
• One-sample t-test