Expected Value
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.

Expected Value of Discrete Random Variable

E[X]=xi×P(xi)E[X] = \sum x_i \times P(x_i)
Where
xix_i
equal to the values that
XX
takes and
P(xi)P(x_i)
is the probability that
XX
takes the value
xix_i

Expected Value of Continuous Random Variable

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.
PDF is a function that specifies the probability of a random variable taking value within a particular range.
E[X]=xminxmaxx×f(x)dxE[X] = \int_{x_{min}}^{x_{max}} x \times f(x) dx
Where
f(x)f(x)
is the PDF of
XX
Last modified 9mo ago