Stonehill College is committed to providing all students equal access to learning opportunities. The Center for Academic Achievement is the campus office that works with students who have disabilities to provide and/or arrange reasonable accommodations. Students registered with The Center, who have a letter requesting accommodations, are encouraged to contact the instructor early in the semester. Students who have, or think they may have, a disability (e.g. psychiatric, attentional, learning, vision, hearing, physical, or systemic), are invited to contact The Center for Academic Achievement for a confidential discussion at 508-565-1208.
| Topic(s) | Chapter(s) | Subtopic(s) |
| Set theory background | n/a | Unions, intersections, and compliments |
| The power set | ||
| Cartesian products | ||
| Finite, countable, and uncountable sets | ||
| Algebras of sets | ||
| Functions | n/a | Abstract definition of a function |
| function images | ||
| function inverse images | ||
| Linear Algebra Review | n/a | Vectors and Matrices |
| Arithmetic Operations on Vectors and Matrices | ||
| Matrix Inverses | ||
| Quadratic Forms | ||
| Probability spaces | 2 | Experiments and outcomes |
| Sample spaces | ||
| Events | ||
| Probability measures | ||
| The Kolmogorov axioms | ||
| Equally likely outcomes and the random sampling experiment | ||
| Conditional probability and independence | 2 | Conditional probability |
| Independence | ||
| Multiplicative and additive rules of probability | ||
| Baye's theorem | ||
| The law of total probability | ||
| Random variables | 2,3 | Discrete - probability mass functions | Continuous - probability density functions |
| Vector valued random variables | ||
| Cumulative distribution functions | ||
| Expectation | ||
| Moments | ||
| Functions of random variables | ||
| Chebychev's theorem | ||
| Discrete probability distributions | 3 | |
| The Bernoulli distribution | ||
| The binomial distribution | ||
| The geometric distribution | ||
| The negative binomial distribution | ||
| The Poisson distribution | ||
| The hypergeometric distribution | ||
| Continuous probability distributions | 4 | |
| The uniform distribution | ||
| The normal or Gaussian distribution | ||
| The gamma distribution | ||
| The beta distribution | ||
| Multivariate probability distributions | 5 | The marginal distribution |
| The conditional distribution | ||
| Independence | ||
| Covariance | ||
| Linear combinations and quadratic forms | ||
| Expected values of linear combinations | ||
| Variances of linear combinations | ||
| The multinomial distribution | ||
| The multivariate normal distribution | ||
| Functions and transformations of random variables | 6 | The distribution of a function of a random variable |
| The method of distribution functions | ||
| The method of transformations | ||
| The method of moment generating functions | ||
| Multivariate transformations and the Jacobian | ||
| Order statistics | ||
| Sampling distributions and the central limit theorem | 7 | Sampling distributions for normal populations |
| The central limit theorem | ||
| The normal approximation to the binomial distribution |