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
Worked Example 4
In a game, \(3\) green balls and \(7\) yellow balls are placed in a bag. A player draws \(4\) balls at random and without replacement. The number of green balls that she draws is denoted by \(G\). Find the probability distribution of \(G\) and show that \(P\left( G\ge 2 \right)=\frac{1}{3}\). Show that \(\text{E}\left( G \right)=\frac{6}{5}\) and find the variance of \(G\).
Alice scores \(5\) points for each green ball that she draws and Bob scores \(2\) points for each yellow ball that he draws.
Alice’s score is denoted by \(A\) and Bob’s score is denoted by \(B\).
Without finding the probability distribution of the number of yellow balls, find the expectation and variance of \(A-B\) if
(a)
Alice and Bob play two separate independent games to decide their scores,
(b)
Alice and Bob decide their score in the same game.
Responses