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NSWMaths AdvancedQuick questions
Year 12: Statistical Analysis
Quick questions on Continuous random variables: probability density functions, cumulative distributions, mean and variance
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 are probability density functions?Show answer
A continuous random variable is described by a probability density function satisfying
What are probabilities as integrals?Show answer
For any interval inside the support, the probability is the area under the density over that interval:
What is cumulative distribution function?Show answer
The cumulative distribution function (cdf) accumulates probability from the left:
What is mean, variance, median, mode?Show answer
The mean (expected value) weights each value by its density and integrates:
What are the standard problem types?Show answer
NESA questions on this dot point fall into a small number of recognisable shapes, and naming the type tells you the first move:
What is sketching the density?Show answer
A quick sketch of over its support guides the work. The total area under the curve must be , the median splits that area in half, and the mode sits under the highest point of the curve. For a symmetric density the mean, median and mode coincide at the centre of symmetry, which can save an integral if you spot the symmetry early.
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