From the course: Probability Foundations for Data Science

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Expectation of continuous random variables

Expectation of continuous random variables

From the course: Probability Foundations for Data Science

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Expectation of continuous random variables

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- [Instructor] Next, let's learn about expectation for continuous random variables. Remember, a continuous random variable contains any value within a specified range or interval of values. For continuous random variables, the expectation is the weighted average of all possible outcomes for the random variable by integrating all those values. Let's look at the formal equation used for finding the expectation of a continuous random variable. You'll have a continuous random variable with infinite possible values in a defined range. This range goes from negative infinity to positive infinity. The expectation is represented by the following probability density function. So here you see if the expectation is equal to the integral from negative infinity to positive infinity with X multiplied by your function F of X. Let's review a few examples to solidify this concept. Let's consider continuous random variable X with the PDF of 2X between the values of zero to one and zero otherwise. To…

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