MathsNet: A Level Statistics 2 Module

S2 Topic 2: Continuous random variables
The variance
The variance, Var(X) of a continuous distribution defined by the pdf f(x) is defined by:
Var(X) = E(X²) - (E(X))² where
and

Find, using calculus, the variance of the distribution described by the pdf:


The mean, E(X) of the distribution is clearly 2. Therefore Var(X) = E(X²) - (E(X))² = 4.8 - 4 = 0.8

Summary

This method uses integration techniques from Pure 1. You will need to know how to integrate basic polyniomials in x such a linear, quadratic or cubic functions, and then how to substitute the limits.
Clearly, looking at the symmetry of the graph of the pdf, the mean can be seen to be 2.

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