MTH 2680 - Introduction to Probability

• Use combination and permutation to solve related problems
• Apply basic set theory concepts to probability problems
• Use basic probability rules
• Use tree diagrams and Venn diagrams to solve probability problems
• Use DeMorgan’s Laws in probability problems
• Identify and solve problems involving conditional probability
• Identify and solve problems involving total probability, Bayes’ Theorem and independence
• Define a discrete random variable and the probability mass function and use them in examples
• Define the cumulative distribution function for discrete random variables and use it to solve related problems
• Define expected value for discrete random variables and use it in related problems
• Solve problems involving conditional expectations of discrete random variables
• Identify and apply the discrete uniform distribution 
• Identify and apply the binomial distribution
• Identify and apply the geometric distribution
• Identify and apply the Poisson distribution
• Identify and apply the negative binomial distribution
• Define a continuous random variable and the probability density function and use them in examples
• Define the cumulative distribution function for continuous random variables and use it to solve related problems
• Define expected value for continuous random variables and use it in related problems
• Use measures of central tendency, including mean, median, midrange, mode, quartiles and percentiles of data sets, and for continuous random variables
• Use measures of dispersion, including variance and standard deviation, both for discrete and continuous random variables
• Define and apply Moment Generating Function of different discrete distributions
• Identify and apply the continuous uniform distribution 
• Identify and apply the normal distribution
• Identify and apply the exponential distribution
• Identify and apply joint (multivariate) distributions of discrete and continuous random variables
• Define and use conditional distributions for both discrete and continuous multivariate
• Define and use independence, covariance and correlation for both discrete and continuous multivariate

• Derivatives of functions, product rule, quotient rule, and chain rule
• Integrals of functions, substitution, integration by parts

• Combinatorial probability: tree diagrams, the multiplication principle, permutation and combination
• General probability: set theory review, basic rules of probability, DeMorgan’s laws, conditional probability, Bayes’ theorem, independence
• Discrete random variables and their distributions: probability mass function, cumulative distribution function, expected value (mean)
• Measures of central tendency: median of a data set, midrange of a data set, mode of a data set, quartiles, and percentiles of a data set
• Measures of dispersion: variance and standard deviation
• Conditional probabilities: conditional expectation
• Different types of discrete distributions: discrete uniform, binomial, geometric, negative binomial, Poisson
• Continuous random variables and their distributions: probability density function, cumulative distribution function, expected value, variance, mode, median, percentiles, moment generating function, conditional probabilities, conditional expectation
• Different types of continuous random variables: continuous uniform, exponential, normal
• Multivariate probability: joint distribution of multivariate discrete, conditional probabilities, independence, covariance, correlation
• Joint distribution of multivariate continuous: conditional probabilities, independence, covariance, correlation