Module Catalogues, Xi'an Jiaotong-Liverpool University   
Module Code: MTH113
Module Title: Introduction to Probability and Statistics
Module Level: Level 1
Module Credits: 5.00
Academic Year: 2020/21
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A
To provide a rigorous introduction to probability and mathematical statistics particularly for math majored students;

To discuss the potential scope of the applications and illustrate typical ways of analysis;

To provide an appropriate technical background for related higher level MTH modules.

Learning outcomes 
A. describe statistical data;

B. apply basic probability theory to solve related problems;

C. provide good knowledge on typical distributions such as Bernoulli, Binomial, Geometric, Uniform, Poisson, Exponential and Normal distributions and their applications;

Method of teaching and learning 
This module will be delivered by a combination of formal lectures and tutorials.
Exploratory Data Analysis

Populations and samples. Measures of location and spread: mean, median, mode, variance and standard deviation, quartiles. Grouped data, frequency histograms, shape, symmetry and skewness. The empirical rule. Graphical methods: Stem-and-leaf plots, Box plots.

Regression and Correlation

Scatter diagrams, linear regression and correlation. Regression predictions - descriptive methods.

Gathering Data

Populations and parameters, sampling, simple random sampling, other sampling designs, observational studies, randomized comparative experiments.

Introduction to Probability

Sample spaces and random events, Venn diagrams. Permutations and combinations. Definitions of probability. Basic probability laws.

Conditional Probability

Conditional probability, probability trees, total probability and Bayes' Theorem. Independence of random events.

Random Variables

Random variables and their distributions. Joint probability distributions. Independence of random variables.

Discrete Distributions

Uniform, Bernoulli, binomial, and Poisson distributions.

Expectations and Variances

Expectations, variances and covariances of random variables and their linear combinations.

Continuous Variables

Continuous random variables and its distributions. Uniform and Normal distributions and their properties. Exponential distribution. Central Limit Theorem.

Sampling Distributions

Distribution of the sample mean from a Normal population. Central Limit Theorem and large sample distribution of the sample mean.
Sampling distribution of the sample proportion.

Estimation and Testing Hypotheses

Introduction to confidence intervals for means and proportions.

Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 


Sequence Method % of Final Mark
1 Midterm Exam 15.00
2 Final Exam 85.00

Module Catalogue generated from SITS CUT-OFF: 6/5/2020 8:41:58 PM