Describing a Discrete Distribution

 

Discrete distributions can be described either graphically or by applying measures of central tendency and variability to the discrete distribution.

 

The histogram is a common way to depict a discrete distribution graphically.

 

The mean or expected value of a discrete distribution is the long-run average of occurrences. Any one trial using a discrete random variable yields only one outcome. However if that process is repeated long enough, the average of the outcomes are most likely to approach a long-run average, expected value, or mean value.

 

The expected value is often referred to as the long-term average or mean. This means that over the long term of doing an experiment over and over, you would expect this average every time you perform a particular experiment.

 

The mean or expected value is computed as follows:

µ = E(x) =

where

            E(x) = long-run average

               x = an outcome

            P(x) = probability of that outcome

 

The expectation of a variable X is a bit like the mean, but for probability distributions. To find the expectation, you multiply each value x by the probability of getting that value, and then sum the results.

 

 

The expected value (mean) of a discrete random variable X, denoted by E(X), is counted as a weighted average of probability distribution. The expected value means the most probable value of discrete random variable, which may occur.[1]