Probability Concepts

Question 0

Total probability rule for expected value

Answer 0

c c
E(X) = E(X|S)P(S) + E(X|S )P(S )
or
E(X) = E(X|S1)P(S1) + E(X|Sn)P(Sn)…

Question 1

Portfolio variance

Answer 1

2 2 2 2
=wA sA + wB sB + 2wAwB CovAB

CovAB= PAB sAsB

Question 2

Conditional expected value

Answer 2

E(X) = E(X1|S)X1 + E(X2|S)X2 + … + P(Xn|S)Xn

Question 3

Multiplicity rule of probability

Answer 3

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

Question 4

Variance of a random value

Answer 4

2
var (x) = E([X-E(X)]    )

The expected value (probability weighted average) of squared deviations from the random variables expected value.

Question 5

Expected value

Answer 5

The expected value of a random variable is the probability weighted average of the possible outcomes of the random variable.

Question 6

Total probability rule

Answer 6

c
P(A) = P(AS) + P(AS )
c c
= P(A|S)P(S) + P(A|S )P(S )

Question 7

Addition rule for probabilities

Answer 7

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

Question 8

Weighted Variance Equation

Answer 8

2 2

Var(x) = P(X1)[X1-E(X)] + … + P(Xn)[Xn-E(X)]

Question 9

Covariance

Answer 9

Cov(Ri,Rj) = E[(Ri-ERi)(Rj-ERj)

A measure of the co-movement between two random variables.

Question 10

Correlation

Answer 10

p(Ri,Rj) = Cov(Ri,Rj) / s(Ri)s(Rj)

s = sigma = standard deviation

A number between -1 and +1 that measures the co-movement between two random variables.

Question 11

Portfolio expected return

Answer 11

Weighted return of a portfolio

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

Question 12

Conditional probability

Answer 12

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

Question 13

Bayes formula

Answer 13

= [(probability of the new information given event)/(unconditional probability of the new information)] x (prior probability of event)

=[P(Info | Event) / P(info)] x P(event)

Question 14

Multiplication rule of counting

Answer 14

Ways to do step 1, times ways to do step 2, times ways to do step n.

Question 15

Assigning members of a group of size n to n slots

Answer 15

n! = n(n-1)(n-2)…1

Question 16

Multi nominal formula

Answer 16

n!/(n1!n2!…nk!)

The number of ways that n objects can be given k labels.

Question 17

Combination formula

Answer 17

The number of ways to choose “r” objects from a total of “n” objects, when the order in which the “r” objects DOESN’T matter.

nCr = n!/(n-r)!r!

Question 18

Permutation formula

Answer 18

The number of ways to choose “r” objects from a total number of “n” objects, where the order in which the “r” objects listed DOES matter.

nPr = n!/(n-r)!

Question 19

Event

Answer 19

A specified set of outcomes of a random variable.

Question 20

Two defining properties of probability

Answer 20

1. P(E) is between 0 and 1

2. The sum of the probabilities of any set of mutually exclusive and exhaustive events equals 1.

Question 21

Probability stated as odds

Answer 21

E = P(E)/[1-P(E)]

Question 22

Dutch Book theorem

Answer 22

Probabilities that are inconsistent create opportunity