Stochastic Methods

Probability theory: Sample spaces, events, and probabilities. Combinatorics. Independent events, conditional probabilities. Discrete and continuous random variables. Common probability distributions, especially the normal, exponential, binomial, and Poisson distributions. Functions of random variables. Expected values, variance, covariance, and correlation. The law of large numbers and the central limit theorem. Stochastic processes, random walks, and Poisson processes. Statistical methods: The Chi-square and t-distributions. Point estimates, unbiased and consistent estimates. Estimation with the maximum likelihood and least squares methods. Confidence intervals and test of significance, especially of the normal, binomial, and Poisson distributions and in situations where the central limit theorem can be applied. Different forms of misleading statistics. Regression analysis.