Let’s Summarize

• When we have a quantitative variable with outcomes that occur as a result of some random process (e.g., rolling a die, choosing a person at random), we call it a random variable.
• Discrete random variables have numeric values that can be listed and often can be counted.
• The probability for each value in a probability distribution is between 0 and 1, inclusive, and the sum of the probabilities in a probability distribution is 1.
• The mean (expected value) of a discrete random variable is found by multiplying each value of the random variable by its associated probability and summing the results.
• The standard deviation of a discrete random variable describes the typical distance a value is from the mean.
• As the number of trials in a probability experiment increases, the mean approaches the theoretical expected value. This is called the law of large numbers.
• There are many different types of discrete random variables, including binomial, geometric, hypergeometric and poisson.  Knowing what type of discrete random variable is being described depends on the properties of the statistical experiment.