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Continuous distributions


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Expectation of a continuous probability distribution


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For a discrete probability distribution, the expectation is defined to be [Equation.] Where [Equation.] is the probability the the random variable X takes the value xi. For a continuous probability distribution this is generalized as follows&: If X is a continuous random variable having probability density function f(x) then [Equation.] Example The continuous random variable X has probability density function given by&: [Equation.]
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

Related articles: (1) Techniques of integration, (2) Continuous distributions