Probability Concepts

Question 1

An uncertain quantity

Answer 1

random variable

Question 2

An observed value of a random variable

Answer 2

outcome

Question 3

Event

Answer 3

a single outcome or a set of outcomes

Question 4

Mutually exclusive events

Answer 4

events that cannot both happen at the same time

Question 5

Exhaustive Events

Answer 5

Events that include all possible outcomes

Question 6

Probability that is established by analyzing past data

Answer 6

Empirical Probability

Question 7

Probability that is determined using a formal reasoning and inspection process

Answer 7

A Priori Probability

Question 8

The probability of an event regardless of the past or future occurrence of other events

Answer 8

Unconditional Probability

Question 9

The occurrence of one event affects the probability of the occurrence of another event

Answer 9

Conditional Probability

Denoted as P(A I B)

Question 10

Multiplication of Probability

Answer 10

P(AB) == P( A I B) * P(B)

Question 11

Probability of A or B

Answer 11

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

Question 12

Probability of A

Answer 12

P(A) = P(A I B1)P(B1) + … +P(A I Bn)P(Bn)

Question 13

The Calculation for Joint Probability

Answer 13

P(A and B) = P(AB) = P( A I B) * P(B)

*the probability that both events will occur

Question 14

An event that has no influence on the occurrence of the others.

Answer 14

Independent events

Question 15

Calculation for Expected Value

Answer 15

E(X) == SUM(P(xi)xi) = P(xa)xa + …+ P(xn)*xn

* the average value for a random variable that results from many experiments.

Question 16

Calculation for Covariance

Answer 16

COV(Ri,Rj) = E {[Ri-E(Ri)] * [Rj-E(Rj)]}
*COV(Ri,Ri) = Var(Ri)

Question 17

Calculating Correlation Coefficient

Answer 17

Corr(Ri,Rj) = Cov(Ri,Rj) / (sigma(Ri)*sigma(Rj))

• has no units
• • If Corr(Ri,Rj) = 0, no correlation exists
• **-1 < Corr(A) < 1

Question 18

Portfolio Expected Return Calculation

Answer 18

E(Rp) = SUM(wiE(Ri)) = w1E(R1) + … + wn*E(Rn)

Question 19

Portfolio Variance

Answer 19

Var(Rp) = (Wa^2sigma^2Ra) + (Wb^2sigma^2Rb) + [2WaWbsigma(Ra)sigma(Rb)*Corr(Ra,Rb)]

Question 20

Bayes Formula

Answer 20

P(A I B) = (P(B I A) / P(A)) * P(B)

Question 21

Combination Formula

Answer 21

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

*order not important

Question 22

Permutation Formula

Answer 22

nPr = n! / (n-r)!

* Order is important