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Quick questions on Discrete random variables: probability distributions, expectation, variance and aX + b - OCR A-Level Further Maths A

3short 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 not checking the distribution sums to one?
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Always verify (or impose) ∑P(X=x)=1\sum \mathrm{P}(X = x) = 1 before computing the mean; an unnormalised distribution gives wrong answers.
What is q1?
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A variable XX has P(X=x)=14\mathrm{P}(X = x) = \tfrac{1}{4} for x=1,2,3,4x = 1, 2, 3, 4. Find E(X)\mathrm{E}(X). [2 marks]
What is q2?
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If Var(X)=4\mathrm{Var}(X) = 4, find Var(2X+5)\mathrm{Var}(2X + 5). [2 marks]

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