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# 3.1 Continuous Probability Distribution and Density Function

#### Continuous Probability Distributions

• The probability distribution for a continuous random variable is a description all the possible values of the random variable, and its corresponding probability.
• Unlike discrete random variables which takes on a set of individual values, a continuous random variable is one that can take any value in an interval of the real number line.

For example, X is a continuous random variable if it takes on any variable in the interval [-0.005,0.005]. In this case, X might be the standard error when measuring using a micrometer screw gauge.

• A continuous random variable has no limit as to the accuracy with which it can be measured. Using the example above, we can have
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