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R9-Probability-1

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msk2222's version from 2018-02-18 15:45

Section 1

Question Answer
Definition of Eventspecified set of outcomes.
Definition of ProbabilityThe probability of any event E is a number between 0 and 1 - 0 ≤ P(E) ≤ 1. The sum of the probabilities of any set of mutually exclusive and exhaustive events equals 1
subjective probability,may adjust an empirical probability to account for perceptions of changing relationships
priori probability/objectivemore narrow range of well-defined problems, we can sometimes deduce probabilities by reasoning about the problem.
unconditional probability, denoted P(A). Unconditional probability/marginal probability is also frequently referred to as
conditional probability, denoted P(A | B)probability of A, given that B has occurred?
joint probability, denoted P(AB)“What is the probability of both A and B happening?”
equation of conditional probabilityP(A | B) = P(AB)/P(B), P(B) ≠ 0  
equation of joint probabilityP(AB) = P(A | B)P(B)  
A or B occurs, or both occur, P(A or B) = P(A) + P(B) – P(AB)  
Two events A and B are independent P(A | B) = P(A) or, equivalently, P(B | A) = P(B).
When two events are independent, the joint probability of A and BP(AB) = P(A)P(B)  
total probability rule. unconditional probability of the event in terms of probabilities conditional on the scenarios.
eqn for totla probability ruleP ( A ) = P ( A S ) + P ( A S C ) = P ( A | S ) P ( S ) + P ( A ∣ ∣ S C ) P ( S C )
memorize

Section 2

Question Answer
Definition of Expected ValueThe 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).
Definition of VarianceThe variance of a random variable is the expected value (the probability-weighted average) of squared deviations from the random variable’s expected value
Definition of Standard DeviationStandard deviation is the positive square root of variance.
conditional expected values.The expected value of a random variable X given an event or scenario S is denoted E(X | S).
Total Probability Rule for Expected Value.E(X) = E(X | S)P(S) + E(X | SC)P(SC)  
conditional variances,variance of EPS given a declining interest rate environment and the variance of EPS given a stable interest rate environment.
main points about conditional variances1) that variance, like expected value, has a conditional counterpart to the unconditional concept and 2) that we can use conditional variance to assess risk given a particular scenario.
memorize

Section 3