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. (“Probability and Statistics with Applications, a Problem-Solving Text”)

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

Links and resources
đź”´ Subscribe to Bill Kinney Math:
đź”´ Subscribe to my Math Blog, Infinity is Really Big:
đź”´ Follow me on Twitter:
đź”´ Follow me on Instagram:
đź”´ You can support me by buying “Infinite Powers, How Calculus Reveals the Secrets of the Universe”, by Steven Strogatz, or anything else you want to buy, starting from this link:
đź”´ Check out my artist son Tyler Kinney’s website:

(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)

As an Amazon Associate I earn from qualifying purchases.

Video source Youtube

Leave a Comment

1 × one =