Overview

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This course is part five of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

This course introduces probability and how it manifests in the world around us. Beginning with discrete random variables, together with their uses in modelling random processes involving chance and variation, you will start to uncover the framework for statistical inference.

Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will introduce discrete and continuous random variables and their applications in a variety of contexts.

Join us as we provide opportunities to develop your skills and confidence in applying mathematics to solve real world problems.

Syllabus

Week 1: Basic probability

Understand the product and sum principles of counting and apply them to solve a variety of counting problems
Recognise when a problem involves a permutation or combination and apply the corresponding formula to count the number of possible results
Understand the concept of probabilities associated with the outcome of a random experiment
Understand the concept of an event as a set of outcomes within the sample space and be able to compute the probabilities associated with events
Use and interpret Venn diagrams to describe compound events
Understand the concepts of independent, mutually exclusive and conditional events and be able to recall and apply the appropriate formula to solve problems in probability
Recall and apply the addition law of probability to solve a variety of problems involving compound events, and
Use and interpret tree diagrams for problems involving conditional probabilities.

Week 2: Discrete random variables

Understand the concept of a random variable and be able to identify/distinguish discrete and continuous random variables
Understand the probability distribution associated with a discrete random variables and its properties
Interpret a variety of representations of discrete random variables including histograms and probability tables
Recall the definition of the mode, median, expected value, variance and standard deviation of a discrete random variable
Calculate the mode, median, expected value, variance and standard deviation of a wide range of discrete random variables
Understand the relation between the properties of a discrete random variable which is a function of another, particularly when that function is linear
Recognize both Bernoulli Binomial experiments and the properties of the random variables associated with each • Apply knowledge of discrete random variables to solve a range of problems.

Week 3: Continuous random variables

Understand the concept of a continuous random variable and its corresponding probability density function
Verify when a function is a valid probability density function
Recall the definition and formula for the mode, median, expected value, variance and standard deviation of a continuous random variable
Calculate the mode, median, expected value, variance and standard deviation for continuous random variables which have a reasonably simple probability density function
Understand the relation between the properties of a continuous random variable which is a function of another
Recognise the properties of the normal distribution
Recall and apply the 68:95:99.7 rule to calculate probabilities of a normal random variable over intervals which are bounded by appropriate intervals
Apply the standard normal transformation to find probabilities and quantiles associated with normal random variables more generally
Use technology to find probabilities and quantiles associated with normal random variables more generally.
Use derivative rules and trigonometric functions, exponential functions and logarithmic functions to solve a variety of problems.

Week 4: Assessment

There is a timed exam.