4. Probability Trees and Conditional Expectations

Question 1

Bayes’ formula

Answer 1

The rule for updating the probability of an event of interest—given a set of prior probabilities for the event, information, and information given the event—if you receive new information.

Question 2

Conditional expected value

Answer 2

The expected value of a stated event given that another event has occurred.

Question 3

Diffuse prior

Answer 3

The assumption of equal prior probabilities.

Question 4

Expected value of a random variable

Answer 4

The probability-weighted average of the possible outcomes of a random variable.

Question 5

Likelihood

Answer 5

The probability of an observation, given a particular set of conditions.

Question 6

Posterior probability

Answer 6

An updated probability that reflects or comes after new information.

Question 7

Total probability rule for expected value

Answer 7

A rule explaining the expected value of a random variable in terms of expected values of the random variable conditional on mutually exclusive and exhaustive scenarios.