Probability and Statistics (2 Credits)

Learning Outcomes:

Compute conditional probabilities directly and using Bayes’ theorem, and check for independence of events; Understand the law of large numbers and the central limit theorem and Compute the covariance and correlation between jointly distributed variables; Construct estimates and predictions using the posterior distribution; Use null hypothesis significance testing (NHST) to test the significance of results, and understand and compute the p-value for these tests; Use specific significance tests including, z-test t-test (one and two sample), chi-squared test; Compute and interpret simple linear regression between two variables

Topics:

1. Counting
2. Random variables, distributions, quantiles, mean variance
3. Conditional probability, Bayes’ theorem, base rate fallacy
4. Joint distributions, covariance, correlation, independence
5. Central limit theorem; Bayesian inference with known priors, probability intervals
6. Conjugate priors
7. Bayesian inference with unknown priors
8. Frequentist significance tests and confidence intervals
9. Resampling methods: bootstrapping
10. Linear regression