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H2 Math Summary Notes
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Pure Mathematics
Unit 1 Inequalities1 Question -
Unit 2 Graphing Techniques7 Questions
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Unit 3 Transformation of Graphs2 Questions
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Unit 4 Functions6 Questions
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Unit 5 APGP & Recurrence Relations6 Questions
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Unit 6 Sigma Notation6 Questions
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Unit 7 Techniques of Differentiation2 Questions
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Unit 8 Applications of Differentiation9 Questions
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Unit 9 Maclaurin Series2 Questions
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Unit 10 Techniques of Integration6 Questions
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Unit 11 Applications of Integration4 Questions
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Unit 12 Differential Equations2 Questions
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Unit 13 Vectors11 Questions
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Unit 14 Complex Numbers6 Questions
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StatisticsUnit 15 Permutation and Combinations7 Questions
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Unit 16 Probability5 Questions
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Unit 17 Discrete Random Variable4 Questions
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Unit 18 Binomial Distribution5 Questions
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Unit 19 Normal Distribution7 Questions
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Unit 20 Sampling and Estimation8 Questions
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Unit 21 Hypothesis Testing6 Questions
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Unit 22 Correlation and Linear Regression5 Questions
Lesson 20,
Question 2
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Worked Example 2
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Given that the random variables \(X\) and \(Y\) have distributions \(N(60, 25)\) and \(N(54, 64)\) respectively, and that \(\bar{X}\) and \(\bar{Y}\) denotes the means of \(7\) independent observations of \(X\) and \(11\) independent observations of \(Y\) respectively.
State the sampling distributions of
(i)
\(\bar{X}-\bar{Y}\)
(ii)
\(2\bar{X}+5\bar{Y}\)
(iii)
\(\frac{{{X}{1}}+{{X}{2}}+{{X}{3}}-{{Y}{1}}-{{Y}{2}}-…-{{Y}{5}}}{8}\)
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