[size=150]In a probability experiment, a random variable (any letter) is used to represent the numerical value associated with each occurrence or outcome in the sample space.[br][br]A random variable is discrete if it has a finite number of possible outcomes and continuous if it has an uncountable number of outcomes. [br][br]The probability density function (PDF) or probability mass function (PMF) is used to describe the probabilities associated with different values of a random variable. The probability mass function (PMF) is used to describe discrete (counted data) probability distributions. Whereas the probability density function (PDF) is used to describe continuous (measured data) probability distributions.[br][br]The expectation or expected value of a random variable is a measure of its average value (mean) of the random variable and is calculated as:[br][br]E(X) = Σ(x)* P(X = x) where X is the random variable, x represents the possible values of X, and P(X = x) is the probability associated with each value. An expected value equal to zero implies that it is a fair event. In business models with profit and loss, the expected value of zero represents the break-even point. [br][br]Content questions students should be able to answer:[br]1) What are PMF and PDF? The probability density function (PDF) or probability mass function (PMF) is used to describe the probabilities associated with different values of a random variable. [br]2) What is the difference between PDF and PMF? PDF is applied in use with continuous random variables and PMF is applied in use with discrete random variables.[br]3) What are the conditions to find the PMF? Px(x) >= 0 and Σ(x) * P(X = x) = 1[/size]