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H2 Math Summary Notes

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  1. Pure Mathematics

    Unit 1 Inequalities
    1 Question
  2. Unit 2 Graphing Techniques
    7 Questions
  3. Unit 3 Transformation of Graphs
    2 Questions
  4. Unit 4 Functions
    6 Questions
  5. Unit 5 APGP & Recurrence Relations
    6 Questions
  6. Unit 6 Sigma Notation
    6 Questions
  7. Unit 7 Techniques of Differentiation
    2 Questions
  8. Unit 8 Applications of Differentiation
    9 Questions
  9. Unit 9 Maclaurin Series
    2 Questions
  10. Unit 10 Techniques of Integration
    6 Questions
  11. Unit 11 Applications of Integration
    4 Questions
  12. Unit 12 Differential Equations
    2 Questions
  13. Unit 13 Vectors
    11 Questions
  14. Unit 14 Complex Numbers
    6 Questions
  15. Statistics
    Unit 15 Permutation and Combinations
    7 Questions
  16. Unit 16 Probability
    5 Questions
  17. Unit 17 Discrete Random Variable
    4 Questions
  18. Unit 18 Binomial Distribution
    5 Questions
  19. Unit 19 Normal Distribution
    7 Questions
  20. Unit 20 Sampling and Estimation
    8 Questions
  21. Unit 21 Hypothesis Testing
    6 Questions
  22. Unit 22 Correlation and Linear Regression
    5 Questions
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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.

Part I

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