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School of Mathematics

# MT1141 Probability and Statistics

Course Facts
• Lecturer:
Dr Peter Neal - Ferranti/C.15, Extension 63634
• Delivery: Semester One
• Lectures: see timetable
• Credits: 10
• Prerequisites: A-Level Mathematics or equivalent
• Teaching and learning methods: Two lectures per week plus one tutorial per week.
• Assessment: End of semester examination (2 hours) 80%. Coursework 20%.
Page Contents

## Course Description

This course gives a general introduction to probability and statistics and is a prerequisite for all future probability and statistics courses.

### Aims

To introduce the basic ideas and techniques of probability and statistics, including the handling of probability distributions, the crucial notions of conditional probability and of independence and the estimation of population means and variances.

### Learning outcomes

On successful completion of the course students will:

• have a good appreciation of the basic laws of probability;
• have the skills to tackle simple problems on probability distributions, conditional probability and independence;
• have a basic understanding and working knowledge of statistics such as sample mean and variance, estimators and unbiasedness.

## Syllabus

• Random experiments, sample space and events, the algebra of events (sets, unions, intersec- tions, complementations, De'Morgans Law) Axioms of probability. Equally likely events. [5]
• Conditional probability of an event. Multiplication rule. Partition theorem, Bayes theorem and applications. Independent events. [4]
• Random variables. Definition. Distribution function. Discrete random variables and prob- ability mass function. Continuous random variables, probability density function and its relation to the distribution function. Calculating probabilities of events defined by random variables. Finding the distribution function of random variables using equivalent events (simple cases). [3]
• Expectation of a random variable and of a function of a random variable, Variance of a random variable. Basic properties of expectation and variance [2]
• The Binomial, Normal and Poisson distributions. [3]
• Random samples and populations. Sample statistics and their distributions. Sample mean as an estimator of the population mean. Properties of the sample mean. Sample variance as an estimator of the population variance. Unbiasedness. [4]
• Bernoulli trials. The geometric and Negative binomial distribution. The sample propor- tion as an estimator to the population proportion. Poisson and Normal approximation to Binomial. [3]

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