Probability Concepts

Question 1

“What is the probability of this event A?”

Example of…

Answer 1

Unconditional probability

Question 2

What is the probability of A, given that B has occurred?

Example of…

Answer 2

Conditional probability

Question 3

Definition of expected value?

Answer 3

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

Question 4

Expected value of ‘X’ notation…

Answer 4

E(X)

Question 5

Expected variance equals…

Answer 5

the sum of probability weighted, squared deviations from the expected value.

Question 6

Calculation of portfolio expected return…

Answer 6

Given a portfolio with n securities, the expected return on the portfolio is a weighted average of the returns on the component securities.

Question 7

Definition of correlation…for variables Ri and Rj

Answer 7

Cov(Ri,Rj) / st.d(Ri)*st.d(Rj)

Correlation is equal to the covariance between the two variables divided by the cross product of their standard deviations.

Question 8

Two random variables X and Y are independent if and only if…

Answer 8

P(X, Y) = P(X)P(Y)

Question 9

Baye’s formula states that given a set of prior probabilities for an event of interest, if you recieve new information, the rule for updating your probability of the event is…

Answer 9

Probability of the new info given event

divided by…

Unconditional probability of the new information

all multiplied by…

Prior probability of event

Question 10

What does a probability distribution specify?

Answer 10

It specifies the probabilities of the possible outcomes of a random variable.

Question 11

What are the two basic types of random variables?

Answer 11

Discrete random variables

Continuous random variables

Question 12

Discrete random variable

Answer 12

Can take on at most a countable number of possible values.

Question 13

Rate of return is an example of what kind of variable?

Answer 13

Continuous random variable

Question 14

What does the cumulative distribution function give us?

Answer 14

It gives us the probability that a random variable X is less than or equal to a particular value x, P(X<=x)

Question 15

How does the cumulative distribution function relate to the probability function?

Answer 15

To find F(x), we sum up, or cumulate, values of the probability function for all outcomes less than or equal to x.

Question 16

What is the simplest of all probability distributions?

Answer 16

Discrete uniform distribution

Question 17

What is the building block of the binomial distribution?

Answer 17

the Bernoulli random variable

Question 18

What is a Bernoulli trial?

Answer 18

A trial, or event that may repeat, that produces one of two outcomes.

Question 19

n! is defined as

Answer 19

n(n-1)(n-2)…1

Question 20

3!

Answer 20

(3)(3-1)(3-2) = (3)(2)(1) = 6

Question 21

Binomial distributions are symmetric when…

Answer 21

When the probability of success on a trial is 0.50, bit is asymmetric or skewed otherwise.

Question 22

A binomial distribution is completely described by two parameters, ____ and ____

Answer 22

n

p

Question 23

Bayes:

Conditional probability of a hypothesis (H) given new evidence (E) depends on three things…

Answer 23

Conditional probability of E given H

The prior probability of the hypothesis H

The prior probability of the evidence E

Question 24

What is ‘base rate fallacy’?

In behavioral finance?

Answer 24

Cognitive error whereby too little weight is placed on the base (original) rate of possibility.

In behavioral finance, it is the tendency for people to erroneously judge the likelihood of a situation by not taking into account all the relevant data and focusing more heavily on new information without acknowledging how the new information impacts the original assumptions.