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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?Show answer
A continuous random variable is described by a probability density function satisfying
What are probabilities as areas?Show answer
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?Show answer
The cumulative distribution function (cdf) is
What is wrong limits on the cdf?Show answer
Integrate from the lower end of the support up to , and remember below the support and above it.
What is q1?Show answer
State the two conditions a probability density function must satisfy. [2 marks]
What is q2?Show answer
How is the median of a continuous variable defined in terms of the cdf? [1 mark]
What is q3?Show answer
Write the expression for of a continuous variable with density . [1 mark]
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