Expected Value of Random Variable
The expected value of a random variable is the weighted average of all possible values of the variable. The weight here means the probability of the random variable taking a specific value.
equal to the values that
is the probability that
takes the value
Since continuous random variables can take uncountably infinitely many values, we cannot talk about a variable taking a specific value. We rather focus on value ranges.
In order to calculate the probability of value ranges, probability density functions (PDF) are used.
is the PDF of