Chapter 4: Probability Trees and Conditional Expectations Flashcards
Expected value of a random variable
The probability-weighted average of the possible outcomes of a random variable.
Variance of a random variable
The expected value (the probability-weighted average) of squared deviations from a random variable’s expected value.
Conditional expected value
The expected value of a stated event given that another event has occurred.
Total probability rule for expected value
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.
Probability tree diagram
A diagram with branches emanating from nodes representing either mutually exclusive chance events or mutually exclusive decisions.
Node
Each value on a binomial tree from which successive moves or outcomes branch.
Conditional variances
The variance of one variable, given the outcome of another.
Bayes’ formula
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.
Prior probabilities
Probabilities reflecting beliefs prior to the arrival of new information.
Likelihood
The probability of an observation, given a particular set of conditions.
Posterior probability
An updated probability that reflects or comes after new information.
Diffuse prior
The assumption of equal prior probabilities.
