# How to Calculate Expected Value of X^2

For a random variable, denoted as X, you can use the following formula to calculate the expected value of X2:

E(X2) = Σx2 * p(x)

where:

• Σ: A symbol that means “summation”
• x: The value of the random variable
• p(x):The probability that the random variable takes on a given value

The following example shows how to use this formula in practice.

## Example: Calculating Expected Value of X2

Suppose we have the following probability distribution table that describes the probability that some random variable, X, takes on various values: To calculate the expected value of X2, we can use the following formula:

E(X2) = Σx2 * p(x)

E(X2) = (0)2*.06 + (1)2*.15 + (2)2*.17 + (3)2*.24 + (4)2*.23 + (5)2*.09 + (6)2*.06

E(X2) = 0 + .15 + .68 + 2.16 + 3.68 + 2.25+ 2.16

E(X2) = 11.08

The expected value of X2 is 11.08.

Note that this random variable is a discrete random variable, which means it can only take on a finite number of values.

If X is a continuous random variable, we must use the following formula to calculate the expected value of X2:

E(X2) = ∫ x2f(x)dx

where:

• ∫ : A symbol that means “integration”
• f(x): The continuous pdf for the random variable X

When calculating the expected value of X2 for a continuous random variable, we typically use statistical software since this computation can be more difficult to perform by hand.