# How to Calculate Expected Value of X^3

For a random variable, denoted as X, you can use the following formula to calculate the expected value of X3:

E(X3) = Σx3 * 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 X3

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 X3, we can use the following formula:

E(X3) = Σx3 * p(x)

E(X3) = (0)3*.06 + (1)3*.15 + (2)3*.17 + (3)3*.24 + (4)3*.23 + (5)3*.09 + (6)3*.06

E(X3) = 0 + .15 + .1.36 + 6.48 + 14.72 + 11.25 + 12.96

E(X3) = 45.596

The expected value of X3 is 45.596.

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 X3:

E(X3) = ∫ x3f(x)dx

where:

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

When calculating the expected value of X3 for a continuous random variable, we typically use statistical software since this computation can be more difficult to perform by hand.