Ch 20: Expected Values

expected value or weighted average

takes into account the varying degrees of importance of the numbers in a data set, gives more weight to the events that are more likely to occur

how to calculate the expected value of a random phenomenon

1. determine all possible outcomes

2. determine the probability of each outcome by determining the probability model

3. multiply each outcome by its probability

4. add these products together

weighted average equation

• the summation: starting from the 1st outcome all the way up to the nth outcome, of everything inside

• P(Xi): the probability of a given outcome of the random variable X

• Xi: a given outcome of the random variable X

Law of Large Numbers

in many independent repetitions of a random phenomenon, the averages or proportions are likely to become more stable as the number of trials increases

the mean of the actually observed outcomes in many repetitions will approach the ________ _______

expected value

the proportion of each possible outcome actually observed in many repetitions will approach the ______ ______________

true probability