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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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