MAT 316 Lecture 3: 15.5 Expected Values of Continuous Random Variables
Document Summary
To find expected values for continuous variables, the formulas are the same as for discrete variables except that all of the sums are replaced with integrals. This means finding expected values is much easier! For a continuous rv x with pdf f(x), Note: the integral can be written from - to when it is for a generic f(x). However, keep in mind that f(x) = 0 for all values of x that are not in the set in the indicator function. In practice, the integral will be over the values in the indicator function, just like sums were. If f(x) is defined on the interval [a, b], then. But since = 0, we don"t need to worry about writing the first and third terms in the above equation. All of the properties and theorems dealing with expected values that you learned previously are still true for continuous random variables.
