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5. The following is called the Bonferroni's inequality: For events A and B, we have that P(ANB) > P(A) + P(B) – 1. a. Prove the Bonferroni inequality. b. Let A and B be events with probabilities P(A) = and P(B) =. Show that R S P(ANB) <

5. The following is called the Bonferroni's inequality: For events A and B, we have that P(ANB) > P(A) + P(B) – 1. a. Prove the Bonferroni inequality. b. Let A and B be events with probabilities P(A) = and P(B) =. Show that R S P(ANB) <

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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5. The following is called the Bonferroni's inequality: For events \( A \) and \( B \), we have that \[ P(A \cap B) \geq P(A) + P(B) - 1. \] a. Prove the Bonferroni inequality. b. Let \( A \) and \( B \) be events with probabilities \( P(A) = \frac{3}{4} \) and \( P(B) = \frac{1}{3} \). Show that \( \frac{1}{12} \leq P(A \cap B) \leq \frac{1}{3} \).
Transcribed Image Text:5. The following is called the Bonferroni's inequality: For events \( A \) and \( B \), we have that \[ P(A \cap B) \geq P(A) + P(B) - 1. \] a. Prove the Bonferroni inequality. b. Let \( A \) and \( B \) be events with probabilities \( P(A) = \frac{3}{4} \) and \( P(B) = \frac{1}{3} \). Show that \( \frac{1}{12} \leq P(A \cap B) \leq \frac{1}{3} \).
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