Continuous distributions
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Variance of a continuous probability distribution.
For a discrete probability distribution we define [Equation.] We generalise this to a continuous probability density function as follows&: If X is a continuous random variable having probability density function f(x) then [Equation.] Example X is a continuous random variable with uniform rectangular distribution defined on the interval (5,20). Sketch the graph of the distribution, define it formally and find E(x) and Var(x). A uniform rectangular distribution means that f(x) = constant over the interval. Since the width of the interval = 15, we have f(x) = 1/15. [Diagram.] Formally, the p.d.f. is defined as [Equation.][Equation.]
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Contents of
Continuous distributions
1 Continuous random variables
2 Continuous distributions. Probability density function
3 Expectation of a continuous probability distribution
4 Variance of a continuous probability distribution.
5 Expectation of a general function of a random variable X
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