### Exam-Ready Series: Further Probability & Statistics Course

• #### Video Tutorials

For each syllabus topic, you will get a series of videos where the core concepts are well-explained with relevant worked examples to give you a deeper understanding

• #### Exam-Style Questions

Learn how to answer typical exam questions with confidence. In this course, you will be exposed to worked example videos which demonstrate how to answer exam questions.

### Course curriculum

• 1
##### Continuous Random Variables
• Introduction
• Piecewise Definition
• Expectation of any function
• Worked Example 1
• The Cumulative Distribution Function
• Worked Example 2
• Median, Quartiles & Percrentiles
• Obtaining the PDF from the CDF
• Finding the CDF and PDF of a related variable
• Worked Example 3
• Worksheet 1
• Woorksheet 2
• 2
##### Inference Using Normal and t-distributions
• The t-distribution
• The mean of a normal population with unknown variance
• Confidence Interval for the Population Mean
• Confidence Interval for the Population Mean – Worked Examples
• Hypothesis Testing (the t-Test)
• Hypothesis Testing (the t-Test) – Worked Example
• Worksheet 1
• Testing the difference between two population means (Worked Example)
• Two-sample t-Tests
• Inference - Hypothesis difference pop means (worked example)
• Calculating Pooled Estimates for the Population Mean
• Two-sample t-Tests (worked example)
• Confidence Interval for the Difference in Population Means (Large Samples)
• Confidence Interval for the Difference in Population Means (Small Samples)
• Worksheet 2
• Paired sample t-tests
• Worksheet 3
• 3
##### Chi-Squared Tests
• Chi-squared - Introduction
• Goodness of Fit Tests (Introduction)
• Chi-squared - Goodness of Fit (Binomial 1)
• Chi-squared - Goodness of Fit (Binomial 2)
• Chi-squared - Goodness of Fit (Geometric)
• Chi-squared - Goodness of Fit (Poisson)
• Worksheet 1
• Chi-squared - Independence (Introduction)
• Worksheet 2
• 4
##### Non-parametric Tests
• Introduction
• Single Sample Sign Test (Large Samples)
• Wilcoxon signed rank test
• Wilcoxon signed rank test (Worked example)
• Wilcoxon signed rank test (Large Samples)
• Paired sample sign test
• Wilcoxon matched pairs signed rank test
• Wilcoxon Rank-Sum Test
• Worksheet 1
• Worksheet 2
• 5
##### Probability Generating Functions
• Introduction
• Calculating Probabilities
• Expectation and variance
• Expectation and variance (worked example)
• Discrete Uniform Distribution
• Binomial Distribution
• Poisson Distribution
• Geometric Distribution
• Sum of indepedent variables
• Worksheet 1
• Worksheet 2