Probability
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1. Basic Probability
  * probability rules (inclusion-exclusion, complement, difference)
  * conditional probability, tree diagrams, multiplication rule
  * sampling with and without replacement
  * total probability, independence
  * Bayes' rule

2. Random Variables
  * discrete RV's - pmf, cdf
  * Bernoulli, Binomial, and Geometric distributions
  * continuous RV's - pdf, cdf
  * Uniform, Gaussian, and Exponential distributions

3. Expectation and Variance
  * formulas for discrete and continuous expectation
  * linearity of expectation: E[aX + bY] = aE[X] + bE[Y]
  * formula for variance, standard deviation
  * scaling and shifting of variance: Var(aX + b) = a^2 Var(X)

4. Joint Probability, Covariance, and Correlation
  * joint discrete probability tables
  * joint pdf's and double integration
  * covariance and correlation formulas (discrete or continuous)
  * independence implies uncorrelated, but uncorrelated does NOT imply independent!
  * Var(X + Y) = Var(X) + Var(Y) + 2 Cov(X, Y)

Statistics
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1. Statistics and Sampling Distributions
  * what is a sample and realization of a sample?
  * mean and variance statistics
  * order statistics (median, quantile, IQR)
  * know the expectation and variance of the mean statistic

2. Estimation, Bias, and Variance
  * what is a parameter, and what is an estimator?
  * what is bias, and what does it mean to be unbiased?
  * bias and variance of the mean statistic for Gaussian and Bernoulli

3. Confidence Intervals
  * what the "alpha" value means
  * Normal approximation vs. Student's t distribution
  * what the critical values mean (z and t)
  * what all of the components in the formulas for Ln and Un are

4. Hypothesis Testing
  * what the H0 and H1 hypotheses are, and what it means to "reject H0"
  * significance level, critical value, and p-value
  * one-sided tests, greater than or less than
  * how to do a t-test for testing the mean statistic of a single sample
  * how to do a t-test for testing the difference in means of two samples