STAT/MATH 511 OVERVIEW STAT 512, J. TEBBS
Here is a summary of some of the main ideas from the prerequisite STAT/MATH 511:
Probability. WMS stands for Wackerly, Mendenhall, and Schaeffer (text).
Chapter 1 (WMS): Overview of basic statistics. We skipped this chapter (STAT 110).
Chapter 2 (WMS): Basic probability theory, set notation, Kolmorogov axioms, com-
plement rule, tools for counting (e.g., combinations, permutations, etc.), conditional
probability, Law of Total Probability, Bayes Rule.
Chapter 3 (WMS): Discrete random variables (positive probability is assigned to spe-
cific points), probability mass functions (pmf), means and variances of discrete random
variables, moment generating functions, Bernoulli trials. Important discrete models:
1. Discrete uniform. Equal probability assigned to each support point.
2. Binomial, b(n, p) (Bernoulli, n= 1). Number of successes out of nBernoulli trials.
3. Geometric, geom(p). Number of Bernoulli trials until 1st success.
4. Negative binomial, nib(r, p). Number of Bernoulli trials until the rth success; gen-
eralisation of the geometric.
5. Hypergeometric, hyper(N, n, r ). Number of Class 1 objects selected from r. Finite
population version of the binomial.
6. Poisson, Poisson(λ). Records counts in a Poisson process over time or space.
Chapter 4 (WMS): Continuous random variables (positive probability is assigned to
intervals; not specific points), probability density functions (pdf), cumulative distribution
functions (cdf), means and variances of continuous random variables, moment generating
functions, Chebyshev. Important continuous models:
1. Uniform, U(θ1, θ2). Pdf is constant over the interval from θ1to θ2.
2. Normal, N(µ, σ2). Most widely used probability model. E(Y) = µand V(Y) = σ2.
Symmetric, unimodal, “bell-shaped.”
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