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Further Probability and Statistics

Quick questions on Discrete random variables explained: H2 Further Mathematics

6short 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 the probability distribution?
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A discrete random variable XX takes a countable set of values, each with a probability P(X=x)\mathrm{P}(X = x). The probabilities must satisfy
What is expectation?
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The expectation (mean) is the probability-weighted average of the values:
What is variance?
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The variance measures spread about the mean. Its definition is Var⁡(X)=E[(X−μ)2]\operatorname{Var}(X) = \mathrm{E}\big[(X - \mu)^2\big], but the computational formula is almost always easier:
What is q1?
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State the computational formula for the variance of a discrete random variable. [1 mark]
What is q2?
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If E(X)=5\mathrm{E}(X) = 5, find E(2X+3)\mathrm{E}(2X + 3). [1 mark]
What is q3?
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If Var⁡(X)=4\operatorname{Var}(X) = 4, find Var⁡(3X−7)\operatorname{Var}(3X - 7). [1 mark]

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