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
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims 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.
 Syllabus Exploratory Data AnalysisPopulations 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 CorrelationScatter diagrams, linear regression and correlation. Regression predictions - descriptive methods.Gathering DataPopulations and parameters, sampling, simple random sampling, other sampling designs, observational studies, randomized comparative experiments.Introduction to ProbabilitySample spaces and random events, Venn diagrams. Permutations and combinations. Definitions of probability. Basic probability laws.Conditional ProbabilityConditional probability, probability trees, total probability and Bayes' Theorem. Independence of random events.Random VariablesRandom variables and their distributions. Joint probability distributions. Independence of random variables.Discrete DistributionsUniform, Bernoulli, binomial, and Poisson distributions.Expectations and VariancesExpectations, variances and covariances of random variables and their linear combinations. Continuous VariablesContinuous random variables and its distributions. Uniform and Normal distributions and their properties. Exponential distribution. Central Limit Theorem. Sampling DistributionsDistribution 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 HypothesesIntroduction 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

## Assessment

 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