MA 2630 - Probability I for AS

• Perform basic set theory operations including union, intersection, and apply them to probability situations
• Understand the differences between mutually exclusive events and independent events and apply this knowledge to probability situations
• Understand the differences and similarities of combinations and permutations and how combinations are used to evaluate probabilities
• Understand the concept of conditional probability and how it extends to the Law of Total Probability and Bayes’ Rule
• Use various discrete probability distributions to determine probabilities
• Use, understand, derive and use discrete probability mass functions, distribution functions, and moment-generating functions
• Understand, derive, and use discrete joint probability functions
• Understand the meaning and relevance of variance and standard deviation and how it relates to probability calculations
• Understand and use the results of the Central Limit Theorem
• Use a transformation function to transform one probability mass function into another

• Algebra
• Calculus

• Union and intersection notation, theory, and examples
• Mutually exclusive events and independent events
• Addition and multiplication rules for probability
• Combinatorics
• Conditional Probability
• Law of Total Probability
• Bayes’ Rule
• Discrete probability distributions such as the binomial, Poisson, negative binomial, uniform, geometric, hypergeometric, etc.
• Discrete probability mass functions
• Discrete cumulative distribution functions
• Discrete moment-generating functions
• Continuous probability distributions such as the Gaussian (normal) distribution, Student-t, chi-squared, F, exponential, gamma, beta, etc.
• Continuous probability density functions
• Continuous cumulative density functions
• Continuous moment-generating functions
• Measures of dispersion (including variance)
• Transformations of random variables