MA 118 - Probability for Business and Liberal Arts
The one-semester course is an introduction to the basic concepts and methods in probability. Upon completion of the course, students will be able to understand and formulate basic problems containing uncertainty, complete routine derivations involving probabilities, and be literate in the language and notation of probability.
- Sample spaces and events: understand the concept of the sample space and events, be able to define probabilities of sample points, and compute probabilities of events.
- Counting: understand the concepts of permutation and combination, recognize problems for which these techniques are appropriate, and correctly apply the corresponding counting techniques or their combinations.
- Conditional probability: understand concept of conditional probability and independent events, be able to determine whether events are independent or not.
- Bayes' Theorem: Bayes' rule and its applications.
- Random variables and probability distributions: understand the concept of a random variable, classify random variables as discrete or continuous, compute probabilities from probability mass (density) functions and cumulative distribution functions.
- Joint probability distributions: compute probabilities (joint and conditional) of two random variables. Test independence of two random variables.
- Means and Variances: be able to compute the expected value and the variance of random variables from the definition, apply their properties to compute mean and variance for linear functions of two or more random variables.
- Covariance and correlation: understand the motivation behind covariance for describing relations between random variables, be able to compute covariance and correlation of two random variables using definitions and properties. Covariance of independent random variables.
- Discrete probability distributions: recognize random variables as having one of the standard probability distributions: uniform distribution, Binomial and Multinomial Distributions, Negative Binomial and Geometric Distributions, and Poisson Distributions. Compute probabilities and statistics of standard discrete random variables.
- Continuous probability distributions: recognize random variables as having one of the standard continuous probability distributions: normal distribution, Gamma and exponential distributions. Compute probabilities and statistics of standard continuous random variables.
- Central limit theorem and its applications: apply central limit theorem to compute normal approximations to random variables. Be familiar with applications of the normal distribution.
- Random sampling: understand basic concepts of random sample and sampling distributions of standard statistics.
Walpole, Ronald E., Raymond H. Myers, Sharon L. Myers, and Keying Ye, Probability and Statistics for Engineers and Scientists, 8th edition, Prentice Hall, 2006.