Study guide of topics covered for Midterm 1
ST 502
Rice textbook chapters covered: 1 - 7.3

--> Probability measures; definitions and properties
--> Conditional probability; definition and law of total probability
--> Bayes' rule, inverse probability 
--> Independence; definition and consequences
--> Random variables; discrete and continuous
--> Probability mass and density functions; defining properties
--> Cumulative distribution function; defining properties
--> Limit theorems
--> Notions of convergence; pointwise, in probability, in distribution, a.s.
--> Law of large numbers
--> Proof of the law of large numbers
--> Markov's inequality and proof
--> Central limit theorem
--> Taylor expansions
--> Moment generating functions and their relation to weak convergence
--> Standardizing a random variable
--> Monte Carlo sampling/integration; importance sampling
--> Distributions derived from the normal distribution; chi-squared, t, and F
--> Heavy tailed versus light tailed distributions
--> Change of variables and transformations of random variables
--> Properties of the sample mean and variance for iid Gaussian data
--> Population parameters versus sample statistics
--> Sampling distribution
--> Finite population sampling, with and without replacement
--> Finite population corrections to sample statistics (sampling without replacement)
--> Expected value and variance of sample statistics
--> Estimation of expected value and variance of sample statistics
--> Normal approximations 
--> Confidence intervals; derivation and interpretation