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Further Probability and Statistics

Quick questions on Continuous random variables explained: H2 Further Mathematics

7short 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 density function?
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A continuous random variable XX is described by a probability density function f(x)\mathrm{f}(x) satisfying
What are probabilities as areas?
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For a continuous variable, the probability of any single value is zero, and a probability over an interval is the area under the density:
What is the cumulative distribution function?
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The cumulative distribution function (cdf) is
What is wrong limits on the cdf?
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Integrate from the lower end of the support up to xx, and remember F=0\mathrm{F} = 0 below the support and 11 above it.
What is q1?
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State the two conditions a probability density function must satisfy. [2 marks]
What is q2?
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How is the median mm of a continuous variable defined in terms of the cdf? [1 mark]
What is q3?
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Write the expression for E(X)\mathrm{E}(X) of a continuous variable with density f\mathrm{f}. [1 mark]

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