Named Continuous Distributions
Understand assumptions and properties of named continuous univariate distributions: normal, beta, gamma, exponential
Solve Problems
Solve problems using joint, marginal, conditional pmf and pdf
Linear
Calculate expectation of linear combinations, covariance, correlation
Transformations
Calculate transformations of jointly distributed random variables
Maximum Likelihood
Solve for the maximum likelihood estimator from a SRS
Normal Distribution
Derive properties of maximum likelihood estimators from SRS of normal distribution
Law of Large Numbers
Apply convergence in probability and distribution to prove the Law of Large Numbers and the Central Limit Theorem
Central Limit Theorem
Derive the 100(1-alpha)% from the pivot derived from the Central Limit Theorem
Probabiltiy
Derive the probability of Type I and Type II Error for simple hypothesis test using test statistic derived from the Central Limit Theorem