Probability Concepts

Question 1

Uncertain value determined by chance

Answer 1

Random variable

Question 2

The realization of a random variable

Answer 2

Outcome

Question 3

A set of one or more outcomes

Answer 3

Event

Question 4

Two events that cannot both occur

Answer 4

Mutually exclusive

Question 5

A set of events that includes all possible outcomes

Answer 5

Exhaustive

Question 6

Two properties of probability

Answer 6

1. The sum of the probabilities of all possible mutually exclusive events is 1.
2. The probability of any event cannot be greater than 1 or less than 0.

Question 7

Measures predetermined probabilities based on well-defined inputs

Answer 7

A priori probability

Question 8

Measures probability from observations or experiments

Answer 8

Empirical probability

Question 9

Measures probability using informed guess

Answer 9

Subjective probability

Question 10

Odds for v. odds against

Answer 10

Odds for = A / B - A, odds against = B / A + B

Question 11

The probability of an event occuring

Answer 11

Unconditional probability

Question 12

The probability of an event A occurring given that event B has occurred

Answer 12

Conditional probability

Question 13

Used to determine to the joint probability of two events

Answer 13

The multiplication rule of probability

P(AB) = P (A|B) x P (B)

or

P(A|B) = P(AB) / P(B)

Question 14

Used to determine the probability that at least one of two events occur

Answer 14

The addition rule of probability

P(A or B) = P(A) + P(B) - P(AB)

Question 15

Used to determine the unconditional probability of an event given condition probabilities

Answer 15

The total probability rule

P(A) = P (A|B1)P(B1) + P(A|B2)P(B2)

B1, B2, etc are mutually exclusive and exhaustive

Question 16

The measure of extent to which two random variables tend to be above and below their respective means for each joint realization.

Answer 16

Covariance

Question 17

Covariance formula

Answer 17

CovA,B = ∑ (Ai - A-bar)(Bi - B-bar) / n - 1

Question 18

The standardized measure of association between two random values

Answer 18

Correlation

Question 19

Correlation formula

Answer 19

Corr (X,Y) = Cov(X,Y) / σA * σB

Question 20

Expected Value of Random Variable

Answer 20

= ∑ Pi(Xi) * Xi

Question 21

Variance of a Random Variable

Answer 21

= ∑ P(Xi)[(Xi-E(X)]^2

Question 22

Expected Return of a 2-asset Portfolio

Answer 22

E(Rp) = w1E(R1) + w2E(R2)

Question 23

Expected Variance of a 2-asset Portfolio

Answer 23

Var(Rp) = (w1^2 * σ1^2) + (w2^2 * σ2^2) + 2(w1w2Cov1,2)

Question 24

Covariance (given joint probability)

Answer 24

=∑ P(Xi, Yi) * (Xi-E(X) * (Yi - E(Y)

Question 25

Bayes’ Formula

Answer 25

= P(I|O) = P(O|I) / P (O) x P (I)

Question 26

Formula to chose a subset of size r from a set of size n when order doesn’t matter

Answer 26

= nCk (combination)

Question 27

Formula to chose a subset of size r from a set of size n when order matters

Answer 27

= nPk (permutation)