Continuous distributions
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Continuous random variables
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A variable X whose values are determined by chance is called a random variable. If the values of X are separated from each other then X is a discrete variable. A continuous random variable is a random variable whose values are not separated from each other. This means that between any two values, a and b, there exists a third value. We have met specific examples of continuous random variables particularly, the normal distribution. The standardized normal distribution is specified by a particular function, f(z), that [Equation goes here &- download the original to see it.] [Diagram goes here &- download the original to see it.] The function, f(z), that gives the characteristic bell&-shaped curve of the normal distribution is an example of a probability density function. As indicated here probabilities are actually given by the area under the curve. For a curve to be considered as giving a probability distribution the total area under it must be equal to 1, since the sum of the probabilities of all possible events must equal 1.
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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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