# Introduction to Probability and Statistics

Masters, *University of Pennsylvania, Department of Electrical/Systems Engineering*, 2018

I was the teaching assistant (TA) for a course Engineering Mathematics (ENM) 503 for the Summer 2018 term. The course was accelerated, meeting 2 times per week for 3+ hours. My responsibilities included

- Leading weekly 1 hour recitation sessions where I would collaboratively solve homework problems on the chalkboard. I tried hard to foster an friendly classroom environment where all students felt comfortable taking part in solving challenging problems.
- I graded extensive weekly problem sets as well as quizzes. Students would take quizzes at the beggning of the class time and I would provide feedback before the class was finished.
- I held office hours every week. Since the class was so small, I had the opportunity to mentor students 1-on-1, especially in during these office hours.

### Course Description

Introduction to combinatorics: the multiplication rule, the pigeonhole principle, permutations, combinations, binomial and multinomial coefficients, recurrence relations, methods of solving recurrence relations, permutations and combinations with repetitions, integer linear equation with unit coefficients, distributing balls into urns, inclusion-exclusion, an introduction to probability. Introduction to Probability: sets, sample setsevents, axioms of probability, simple results, equally likely outcomes, probability as a continuous set function and probability as a measure of belief, conditional probability, independent events, Bayesâ€™ formula, inverting probability trees. Random Variables: discrete and continuous, expected values, functions of random variables, variance. Some Special Discrete Random Variables: Bernoulli, Binomial, Poisson, Geometric, Pascal (Negative Binomial) Hypergeometric and Poisson. Some Special Continuous Random Variables: Uniform, Exponential, Gamma, Erlang, Normal, Beta and Triangular. Joint distribution functions, minimum and maximum of independent random variables, sums of independent random variables, reproduction properties. Properties of Expectation: sums of random variables, covariance, variance of sums and correlations, moment-generating function. Limit theorems: Chebyshevâ€™s inequality, law of large numbers and the central-limit theorem.