5.1 Expected Value

probability model

a function that associates a probability (P) with each value of a discrete random variable X, denoted P(X = x), or with any interval of values of a continuous random variable

E(X) = μ= ∑ xP(x)

the formula for the expected value of a discrete random variable

expected value

the theoretical long-run average value of a model, also considered the center of the model - denoted as E(X), or μ

discrete random variable

a random variable where there are a discrete (or finite) number of outcomes

continuous random variable

a random variable with an infinite number of possible outcomes between a given set of bounds

Var(X) = σ² = ∑(x−μ)²P(x)

formula for the variance of a discrete random variable - notice the expected value of the random variable is used in the calculation

variance

the expected value of the squared deviation from the mean - denoted by Var(X) or σ²

random variable

a variable that represents all possible probabilities of all possible outcomes of a random event - these are denoted by a capital letter such as X, Y, or Z

standard deviation

the square root of the variance; describes the spread of the model - denoted S D(X) or σ

SD(X) = √Var(X)

the formula for the standard deviation of a discrete random variable