Probability

Question 1

Define Joint Probability - multiplication rule

Answer 1

The joint probability of two events is the probability that they will both occur. The multiplication rule of probability is used to determine the joint probability of two events:

P(AB) = P(A | B) × P(B)

Or

P(B | A) × P(A)

Question 2

Describe Parametric and noparametric tests

Answer 2

Parametric tests rely on assumptions regarding the distribution of the population and are specific to population parameters.

Nonparametric tests either do not consider a particular population parameter or have few assumptions about the population that is sampled - Nonparametric tests are primarily concerned with ranks, signs, or groups, and they are used when numerical parameters are not known or do not meet assumptions about distributions.

i

Question 3

Probability of A given B - Conditional Probability

Answer 3

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

Questions may reference scenarios where the actor (for lack of a better term) is doing 2 things. for example, Jon picked a stock and it had a positive return.

Question 4

Addition Rule - Probability of one of two events occurring

Answer 4

If the events are not mutually exclusive, double counting must be avoided by subtracting the joint probability that both A and B will occur from the sum of the unconditional probabilities. This is reflected in the following general expression for the addition rule:

P(A or B) = P(A) + P(B) – P(AB)

If mutually exclusive, P(A or B) = P(A) + P(B)

Question 5

Joint Probability of any # of independent events

Answer 5

The multiplication rule we used to calculate the joint probability of two independent events may be applied to any number of independent events

The probability of rolling 3 4s on a die is 1/61/61/6

Question 6

What type of probability classification does “likelyhood” fall under?

Answer 6

conditional probability - the probability of an observation, given a particular set of conditions

Question 7

Binomial Distribution (“Bernoulli trial”)

Answer 7

1 - Recognize if the question is asking for success or failure in a given # of attempts (i.e. wins and losses)

2 - Each attempt is independent

3 - Looking for the portability of x successes in n trials

Formula

[n! / ((n - x)! * x!) * p^x * (1 - p)^n-x

Note p is the probability of success.

Question 8

Define a discrete random variable

Answer 8

A discrete random variable is a random variable that can take on a countable number of possible values. i.e. The number of days on which the DJIA experienced an increase since 2013

Question 9

Empirical Probability

Answer 9

An empirical probability is a probability estimated from data as a relative frequency of occurrence.

Question 10

a priori probability

Answer 10

An a priori probability is a probability obtained based on logical analysis.

Question 11

Data Mining Bias

Answer 11

Data mining bias comes from overuse or misuse of the data and can result in finding models or patterns where none exist.

Question 12

sample selection bias

Answer 12

Sample selection bias often results when data availability leads to certain data being excluded from the analysis.

Question 13

Look ahead bias

Answer 13

Look-ahead bias exists if the model uses data not available (forecasted data) to the analyst at the time the analyst acts on the model.