The expected value of a discrete random variable ‘x’ is given byReview LaterP(x)∑ x P(x)∫ x P(x) dx∑ P(x)

The expected value of a discrete random variable 'x' is given by the sum of the product of each outcome and its probability. This can be mathematically represented as:

E(x) = ∑ x P(x)

Here, E(x) represents the expected value, 'x' represents each outcome of the random variable, and P(x) represents the probability of each outcome.

This formula is used to calculate the mean of a probability distribution. It gives us a measure of the 'center' of the distribution.

In the case of a continuous random variable, the expected value is given by the integral of the product of the outcome and its probability density function, represented as:

E(x) = ∫ x P(x) dx

Here, the integral sign ∫ represents the sum of an infinite number of infinitesimally small areas under the curve of the function xP(x), and dx represents an infinitesimally small change in x.