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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 19,
Question 6
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Worked Example 6
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The random variable \(X\) is normally distributed with mean \(135\) variance \({{\sigma }^{2}}\).
(i)
Given that \(\text{P}\left( 127a \right)=0.3865\), show that \(\sigma =10.68\), correct to the \(2\) decimal places, and find the value of the constant \(a\).
\(X\) is related to a normal random variable \(Y\) by formula \(X={{Y}_{1}}+{{Y}_{2}}-4\), where \({{Y}_{1}}\) and \({{Y}_{2}}\) are two independent observations of \(Y\).
(ii)
Find \(\text{E}\left( Y \right)\) and \(\text{Var}\left( Y \right)\).
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