# Probability and Statistics Exam 1 Review Problems and Solutions

Author: Bill Kinney

Types of Probability and Statistics Exam 1 Review Problems and Solutions: 1) Venn Diagram, 2) Combinatorial Probability, 3) Geometric, Binomial, Poisson, and Exponential Random Variables, 4) Bayes’ Theorem, 5) Means and Moment Generating Functions, 6) Variance Computational Formula. https://amzn.to/3Hd7tFN (“Probability and Statistics with Applications, a Problem-Solving Text”)

This is for a Calculus-based Probability and Statistics Course for Scientists and Engineers.

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⏱️TIMESTAMPS⏱️
(0:00) Types of problems
(0:43) Venn diagram problem (mutually exclusive events and complement rule)
(5:00) Combinatorial probability problem 1 (combinations)
(12:29) Combinatorial probability problem 2 (combinations)
(16:59) Binomial distribution (binomial random variable)
(21:19) Bayes’ Theorem (disease testing with a tree diagram)
(29:11) Geometric distribution (geometric random variable)
(33:18) Discrete random variable probability mass function (PMF) and cumulative distribution function (CDF)
(35:57) Definition of mean (expected value) of a discrete random variable
(37:57) Moment generating function (MGF) and the mean
(41:12) Variance computational formula: Var(X) = E[X^2] – (E[X])^2
(44:04) Poisson distribution (Poisson random variable)
(49:41) Exponential distribution (exponential random variable), a continuous random variable
(54:16) Continuous random variable CDF, probability, and mean (expected value)

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