Prescribing exam practice questions

Exam 1 Questions

Note: All problems are from Hogg, McKean, and Craig (7th Ed.). have a distribution that is b(n, p). a) Prove that Y n /n converges in probability to p. This result is one form of the week law of large numbers.

Probability Exam Questions with Solutions

The exam questions accompany the basic probability material in the chapters 7-14 of my textbook Understanding Probability, third edition, Cambridge University Press, 2012. The simulation-based chapters 1-6 of the book present many probability applications from everyday life to help the beginning student develop a feel for probabilities. Moreover, the book gives an introduction to discrete-time ...

Sample Quiz and Exam Questions

Old Exam Questions in Distributed Information Systems

Practice Algebra Qualifying Exam Solutions

1. Let A be an n× n matrix with complex coefficients. Define trA to be the sum of the diagonal elements. Show that trA is invariant under conjugation, i.e., trA = trPAP for all invertible n× n matrices P. Proof. Let P be an invertible matrix. Let ~pk be the k-th row of P, ~qj the j-th column of P, and ~ ai the i-th column of A. The k-th row of the matrix PA is 〈~pk · ~ a1, . . . ,~pk · ~ an〉. S...