Further Probability & Statistics
For Exam Success in CAIE A Level Further Mathematics (9231)
This is the only course which you need to master A Level Further Probability Statistics and prepare for the for CAIE A Level Further Mathematics (9231) exams. Besides learning the new chapters of the course, you will also gain a better understanding of the concepts you learnt in A Level Probability and Statistics 1 & 2 (9709). There will be worked solutions in this course to ensure that you get sufficient practice and exposure to exam-style questions. Enroll today!
Key concepts of each topic explained
How to handle common exam questions
High-quality questions to ensure sufficient practice
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
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
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
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
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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