H2 Math Summary Notes

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Pure Mathematics
Unit 1 Inequalities
Basics of Test Point Method
Unit 2 Graphing Techniques
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Unit 3 Transformation of Graphs
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Unit 4 Functions
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How to Use GC to Plot an Inverse Graph
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Unit 5 APGP & Recurrence Relations
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Unit 6 Sigma Notation
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Unit 7 Techniques of Differentiation
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Unit 8 Applications of Differentiation
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Unit 9 Maclaurin Series
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Unit 10 Techniques of Integration
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Unit 11 Applications of Integration
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Unit 12 Differential Equations
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Unit 13 Vectors
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Unit 14 Complex Numbers
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Statistics
Unit 15 Permutation and Combinations
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Unit 16 Probability
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Unit 17 Discrete Random Variable
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Unit 18 Binomial Distribution
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Unit 19 Normal Distribution
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Unit 20 Sampling and Estimation
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Unit 21 Hypothesis Testing
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Unit 22 Correlation and Linear Regression
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Worked Example 6

H2 Math Summary Notes Unit 19 Normal Distribution Worked Example 6

The random variable [latex]X[/latex] is normally distributed with mean [latex]135[/latex] variance [latex]{{\sigma }^{2}}[/latex].

(i)

Given that [latex]\text{P}\left( 127a \right)=0.3865[/latex], show that [latex]\sigma =10.68[/latex], correct to the [latex]2[/latex] decimal places, and find the value of the constant [latex]a[/latex].

[latex]X[/latex] is related to a normal random variable [latex]Y[/latex] by formula [latex]X={{Y}_{1}}+{{Y}_{2}}-4[/latex], where [latex]{{Y}_{1}}[/latex] and [latex]{{Y}_{2}}[/latex] are two independent observations of [latex]Y[/latex].

(ii)

Find [latex]\text{E}\left( Y \right)[/latex] and [latex]\text{Var}\left( Y \right)[/latex].

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