Using Probability to Make Decisions

Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

Find the expected payoff for a game of chance.

Evaluate and compare strategies on the basis of expected values.

Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.