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VICMath MethodsQuick questions

Unit 3

Quick questions on Discrete random variables: VCE Math Methods Unit 3

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is off-by-one on cumulative probabilities for integer XX?
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P(X<3)=P(X≤2)P(X < 3) = P(X \leq 2), not P(X≤3)P(X \leq 3).
What is q1?
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A variable has P(X=1)=0.2P(X=1)=0.2, P(X=2)=0.5P(X=2)=0.5, P(X=3)=0.3P(X=3)=0.3. Find E(X)E(X). [2 marks]
What is q2?
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For the same distribution, find Var(X)\mathrm{Var}(X). [3 marks]
What is q3?
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Given E(X)=6E(X) = 6 and Var(X)=4\mathrm{Var}(X) = 4, find E(3X+2)E(3X + 2) and Var(3X+2)\mathrm{Var}(3X + 2). [2+2 marks]

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