CFA 8: Probability Concepts Flashcards
random variable
Probability, Expected Value, and Variance
A quantity whose outcomes are uncertain.
outcomes
Probability, Expected Value, and Variance
Possible values
event
Probability, Expected Value, and Variance
A specified set of outcomes.
probability
Probability, Expected Value, and Variance
A number between 0 and 1 that measures the chance taht a stated event will occur.
pairs arbitrage trade
Probability, Expected Value, and Variance
A trade in two closesly related stocks involving the short sale of one and the purchase of the other.
Dutch Book Theorem
Probability, Expected Value, and Variance
A result in probability theory stating that inconsistent porbabilities create profit opportunities.
unconditional probability
Probability, Expected Value, and Variance
The probability of an event NOT conditioned on another event.
conditional probability
Probability, Expected Value, and Variance
The conditional probability of A given that B has occurred is equal to the join probability of A and B divided by the probability of B (assumed not to equal 0).
joint probability
Probability, Expected Value, and Variance
The probability of the joint occurrence of stated events.
addition rule for probabilities
Probability, Expected Value, and Variance
A principle stating that the probability that A or B occurs (both occur) equals the probability that A occurs, plus the probability that B occurs, minus the probability that both A and B occur
independent events
Probability, Expected Value, and Variance
Two events are independent if and only if P(A | B) = P(A) or, equivalently, P(B | A) = P(B).
dependent events
Probability, Expected Value, and Variance
When two events are not independent. The probability of occurence of one is related to the occurrence of the other.
expected value of a random variable
Probability, Expected Value, and Variance
The expected value of a random variable is the probability-weighted average of the possible outcomes of the random variable. For a random variable X, the expected value of X is denoted E(X).
conditional expected values
Probability, Expected Value, and Variance
The expected value of a stated event given that another event has occured.
total probability rule for expected value
Probability, Expected Value, and Variance
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.
conditional variances
Probability, Expected Value, and Variance
The variance of one variable given the outcome of another.
Properties of Correlation
Portfolio Expected Return and Variance of Return
1) Correlation is a number between -1 and +1 for two random variables, X and Y:
- 1 less than or equal to p(X,Y) less than or equal to +1
2) A correlation of 0 (uncorrelated variables) indicates an absence of any linear (straight-line) relationship between the variables. Increasingly positive correlation indicates an increasingly strong positive linear relationship (up to 1, which indicates a perfect linear relationship). Increasingly negative correlation indicates an increasingly strong negative (inverse) linear relationship (down to -1, which indicates a perfect inverse linear relationship).
posterior probability
Topics in Probability
An updated probability that reflects or comes after new information.
combination
Topics in Probability
A listing in which the order of the listed items does not matter.
permutation
Topics in Probability
An ordered listing.
