01The Poisson Distribution
Calculating Poisson probabilities Po(λ) · Mean and variance of a Poisson distribution both equal to λ · Poisson distribution as a model for random events · Poisson approximation to the binomial distribution …
Linear Combinations of Random Variables
E(aX + b) and Var(aX + b) · E(aX + bY) and Var(aX + bY) for independent X and Y · Linear combination of normal random variables is normal · Sum of independent Poisson random variables is Poisson
Continuous Random Variables
Probability density functions and their properties · Using a PDF to find probabilities, mean, variance and median
Sampling and Estimation
Distinction between sample and population; need for random sampling · Identifying flaws in sampling methods · Sample mean as a random variable: E(X-bar) = μ, Var(X-bar) = σ^2/n · Distribution of sample mean when population is normal …
Hypothesis Tests
Nature of hypothesis testing; one-tailed and two-tailed tests · Null and alternative hypotheses, significance level, critical region · Hypothesis tests for binomial and Poisson distributions · Hypothesis test for a population mean (normal distribution or large sample) …