The formula means that we multiply each value, x, in the support by its respective probability, f ( x), and then add them all together. It can be seen as an average value but weighted by the likelihood of the value. In Example 3-1 we were given the following discrete probability distribution: What is the expected value?
For a discrete random variable, the expected value, usually denoted as μ or E ( X), is calculated using: The formula means that we multiply each value, x, in the support by its respective probability, f ( x), and then add them all together. It can be seen as an average value but weighted by the likelihood of the value.
The formula means that we multiply each value, x, in the support by its respective probability, f ( x), and then add them all together. It can be seen as an average value but weighted by the likelihood of the value. In Example 3-1 we were given the following discrete probability distribution:
The variance of a discrete random variable is given by: σ 2 = Var ( X) = ∑ ( x i − μ) 2 f ( x i) The formula means that we take each value of x, subtract the expected value, square that value and multiply that value by its probability. Then sum all of those values. There is an easier form of this formula we can use.