Course curriculum
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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
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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
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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
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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
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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
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