Vol. 1 Probability Concepts

Question 1

(probability concepts)
An investor’s concerns center on returns.
The return on a risk asset is an example of _____?

Answer 1

[a] random variable

Question 2

(probability concepts)
Random variable [definition]

Answer 2

A quantity whose future outcomes are uncertain

Question 3

(probability concepts)
outcome [definition]

Answer 3

a possible value of a random variable

Question 4

(probability concepts)
event [definition]

Answer 4

a specified set out outcomes

Question 5

(probability concepts)
probability [definition]

Answer 5

a number between 0 and 1 that measures the change that a stated event will occur

Question 6

(probability concepts)
two defining properties of probability

Answer 6

1: the probability of any event E is a number between 0 and 1: 0 <= P(E) <= 1;

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

Question 7

(probability concepts)
mutually exclusive [definition]

Answer 7

means that only one event can occur at a time

Question 8

(probability concepts)
exhaustive [definition]

Answer 8

means that the events cover all possible outcomes

Question 9

(probability concepts)
empirical probability [definition]

Answer 9

the probability of an event as a relative frequency of occurrence based on historical data

Question 10

(probability concepts)
subjective probability [definition]

Answer 10

a personal assessment of probability without reference to any particular data.

Question 11

(probability concepts)
a prior probability [definition]

Answer 11

a deduction of the probability based upon logical analysis rather than on observation or personal judgment

Question 12

(probability concepts)
estimate the probability of flipping a coin and getting exactly two heads out of five flips [empirical probability]

Answer 12

perform the experiment 100 times (five flips each time) and find you get 33. so, 33/100

Question 13

(probability concepts)
estimate the probability of flipping a coin and getting exactly two heads out of five flips [a priori probability]

Answer 13

assume that binomial probability function applies, and calculate

Question 14

(probability concepts)
If you have a 40% probability of passing a course, then what are the odds of passing?

Answer 14

p/(1-p = 0.4/0.6 = 0.667

Question 15

(probability concepts)
What is the probability that the stock earns a return above the risk-free rate (event A)?

Answer 15

an unconditional probability that can be viewed as the ratio of two quantities, wit the numerator as the sum of the probabilities of stock returns above the risk-free rate. The denominator is 1, as it is the sum of the probabilities of all possible returns.

Question 16

(probability concepts)
binomial probability distribution [formula]

Answer 16

Question 17

(probability concepts)
Multiplication rule for probability

Answer 17

The joint probability of A and B can be expressed as
P(AB) = P(A | B) P(B)

Question 18

(probability concepts)
Addition rule for probabilities

Answer 18

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

Question 19

(probability concepts)
Multiplication rule for independent events

Answer 19

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

Question 20

(probability concepts)
Total probability rule

Answer 20

Explains the unconditional probability of the event in terms of probabilities conditional on the scenarios

Question 21

(probability concepts)
Total probability rule for two scenarios

Answer 21

Question 22

(probability concepts)
Total probability rule for n scenarios

Answer 22

Question 23

(probability concepts)
Bayes’ Formula [description]

Answer 23

Bayes’ formula make use of the total probability rule. Bayes reverses the “given that” information. It is a rational method for adjusting our viewpoints as we confront new information.

Question 24

(probability concepts)
Bayes’ formula [calculation]

Answer 24

P( Event | Information) = [P ( Info | Event) / P(Info)] * P(Event)

Question 25

(probability concepts)
conditional probabilities of an observation are sometimes referred to as ___________

Answer 25

likelihoods

Question 26

(probability concepts)
___________ are required for updating the probability

Answer 26

likelihoods

Question 27

(probability concepts)
On the basis of your interpretation of the announcement, you update that probability. This updated probability is called the _____________ because it reflects or comes after the new information.

Answer 27

posterior probability