Suppose that 100 students take a test in a class. Each student has a 2/3 probability of passing the test, and the passing of the test is independent over the students. You wish to bound (from above) the probability that no more than 30 of the students pass the test. a. Use the Markov inequality to bound this probability. b. Use the Chebyshev inequality to bound this probability. c. Use the Chernoff bound to bound this probability.

Suppose that 100 students take a test in a class. Each student has a 2/3 probability of passing the test, and the passing of the test is independent over the students. You wish to bound (from above) the probability that no more than 30 of the students pass the test. a. Use the Markov inequality to bound this probability. b. Use the Chebyshev inequality to bound this probability. c. Use the Chernoff bound to bound this probability.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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