Prof Fricker
December 2011
What You Need to Know from OA3101 for OA3102
1. Basic probability (Wackerly, Mendenhall, and Scheaffer chapter 2)
a. Familiarity with probability axioms and rules
b. Ability to calculate the probability of various types of compound events from
simple events
2. Discrete and continuous random variables (WM&S chapters 3.1-3.5, 3.8, and 4.1-4.5)
a. Understanding of pmfs/pdfs and cdfs
i. Ability to derive cdf from pmf or pdf
ii. Ability to calculate the probability of a particular outcome or range of
outcomes
iii. Ability to calculate expected values and variances (and standard
deviations), including “shortcut formula” for variance, for discrete and
continuous r.v.s
b. Detailed knowledge of specific distributions: Bernoulli, bionomial, Poisson,
uniform, normal, exponential
i. Basic distributional notation, such as N(,2), U(0,1), etc.
ii. Expression for each distribution’s pmf/pdf
iii. Expected values and variances along with standard notation: E(X), Var(X),
etc.
iv. Under what conditions each distribution is appropriate for modeling realworld phenomena
v. Understanding the concept of distributional parameters (E.g., How do the
distributions change when parameters are changed? For the normal
distribution, what does it mean to say that E(X)=? What does  mean in
the exponential? Etc.)
vi. Binomial approximation to Poisson
c. Specifically for the normal distribution:
i. Ability to standardize and use standardized values to calculate
probabilities
ii. How to find critical values for a given tail probability and vice versa
iii. Normal approximation to the binomial, including continuity correction
3. Jointly distributed random variables (WM&S chapters 5.1-5.4, 5.7)
a. Understanding, both quantitatively and intuitively, of independence of two
random variables.
b. Ability to calculate and interpret covariance and correlation
c. Intuitive understanding of joint, marginal, and conditional distributions
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Prof Fricker
December 2011
4. Distributions of linear combinations of random variables (WM&S chapter 5.8)
a. Rules for calculating the expected value and variance of a linear combination of
random variables, particularly the sum and mean of n iid r.v.s
b. Ability to calculate the mean and variance for the sample mean, for the
differences of two iid r.v.s, etc.
c. Expression for the variance of two dependent r.v.s
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