Basic Probability and Discrete Probability Distributions

Basic Probability Concepts
Understanding of probability fundamentals, including:
- Probability: Numerical representation (0 to 1) of the possibility of an event occurring.
- Event: Outcome of a variable.
Approaches to Assessing Probability
A priori Classical Probability: Based on prior knowledge.
Empirical Classical Probability: Based on observed data.
Subjective Probability: Based on personal judgment.
Types of Events
Simple Event: One characteristic outcome.
Complement of an Event (A'): Outcomes not part of event A.
Joint Event (A ∩ B): Two or more characteristics occurring simultaneously.
Mutually Exclusive Events: Events that cannot occur together (e.g., Male vs. Female).
Collectively Exhaustive Events: One event must occur (e.g., loyalty program member vs. non-member).
Probability Calculations
Joint Probability: P(A and B).
Marginal Probability: P(A).
General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B).
Conditional Probability: P(A | B), the probability of A given B has occurred.
Decision Trees: Alternative to contingency tables for visualizing probabilities.
Statistical Independence: Events A and B are independent if the occurrence of one does not affect the other.
Counting Rules: Methods to calculate possible outcomes.
Rule 1: Outcomes for k mutually exclusive events over n trials.
Rule 2: Outcomes for k1, k2, … kn events across trials.
Rule 3: Arrangements of n items: n!.
Rule 4: Permutations of X from n objects.
Rule 5: Combinations of X from n objects ignoring order.
Discrete Probability Distributions
Defines expectations and variances for discrete outcomes.
Expected Value (Mean) Calculation: E(X) = sum of values x their probabilities.
Variance and Standard Deviation Definitions and Calculations.
Portfolio Calculations for expected return and risk using weight averages.