## 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