# Probability and Statistics for Actuarial Science - MACT7290

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## Module delivery information

Location Term Level1 Credits (ECTS)2 Current Convenor3 2022 to 2023
Canterbury
Autumn Term 7 30 (15) Owen Lyne

## Overview

The curriculum covers parts of the professional curriculum of the Institute and Faculty of Actuaries syllabus CS1, and it introduces (and revises for some students) the essentials of probability and classical (frequentist) statistical inference.
Probability: review of elementary probability, concept of random variable, discrete and continuous probability distributions, cumulative distribution function, expectation and variance, joint distributions, marginal and conditional distributions, generating functions and transformation of random variables.
Statistics: sampling distributions, point estimation, method of moment and maximum likelihood estimation, confidence intervals, hypothesis testing, association between variables and linear regression.

## Details

### Contact hours

Total contact hours: 75
Private study hours: 225
Total number of study hours: 300

## Method of assessment

80% examination, 20% coursework

Miller, I. and Miller, M. (2003) [Recommended]
John E. Freund's Mathematical Statistics with Applications. 7th international edition.
Pearson Education, Prentice Hall, New Jersey.

Hogg, R., Craig, A. and McKean, J. (2013) [Background]
Introduction to Mathematical Statistics. 7th international edition.
Pearson Education, Prentice Hall, New Jersey.
Larson, H. J. (1982) [Background]
Introduction to Probability Theory and Statistical Inference. 3rd edition.
Wiley, New York.
Spiegel, M. R, Schiller, J. and Alu Srinivasan, R. (2013) [Background]
Schaum's Outline of Probability and Statistics. 4th edition.
McGraw-Hill, New York

## Learning outcomes

The intended subject specific learning outcomes. On successfully completing the module students will:
1 have a systematic knowledge of probability theory and statistical inference
2 be able to use mathematical techniques to manipulate joint, marginal and conditional probability distributions, to derive distributions of transformed random variables, to
analyse associations between random variables, and study the effects of one or more explanatory variables on the response variables through linear regression modeling
3 be able to use a comprehensive range of mathematical techniques to calculate point and interval estimates of parameters and to perform tests of hypotheses
4 be able to select and apply the above techniques to critically evaluate complex real world problems and find suitable solutions.

The intended generic learning outcomes. On successfully completing the module students will:
1 have developed their understanding of probability and statistics;
2 have critically applied a range of mathematical techniques to solve complex statistical problems
3 have developed their ability to critically evaluate and abstract the essentials of problems and to formulate them mathematically
4 have developed high-level skills in numeracy and problem solving
5 have enhanced their study skills and ability to work with relatively little supervision