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Prove the Bonferroni inequalities, which state that for any events {A1, A2, An} CF and any integer ke {1, 2, ..., n}, k Pr(UA) ≤ (-1)-1 Σ l=1 k Pr(U-14;) ≥ Σ(−1)²-1 2 l=1 SC1,2,...,n|| Sl Σ SC1,2,...,n||S|=t Pr(njes Aj)if k is odd Pr(njes Aj), if k is even

Prove the Bonferroni inequalities, which state that for any events {A1, A2, An} CF and any integer ke {1, 2, ..., n}, k Pr(UA) ≤ (-1)-1 Σ l=1 k Pr(U-14;) ≥ Σ(−1)²-1 2 l=1 SC1,2,...,n|| Sl Σ SC1,2,...,n||S|=t Pr(njes Aj)if k is odd Pr(njes Aj), if k is even

A First Course in Probability (10th Edition)
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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Prove the Bonferroni inequalities, which state that for any events {A1, A2, ..., An} CF and any integer ke {1, 2,..., n}, k Pr(U²₁_₁A₁) ≤ Σ(-1)²-1 l=1 k Pr(U²1 Aj) ≥ Σ(−1)²-1 l=1 Σ SC1,2,...,n|| St Pr(Njës A;)if k is odd Σ Pr(njes Aj), if k is even SC1,2,...,n||S|=l
Transcribed Image Text:Prove the Bonferroni inequalities, which state that for any events {A1, A2, ..., An} CF and any integer ke {1, 2,..., n}, k Pr(U²₁_₁A₁) ≤ Σ(-1)²-1 l=1 k Pr(U²1 Aj) ≥ Σ(−1)²-1 l=1 Σ SC1,2,...,n|| St Pr(Njës A;)if k is odd Σ Pr(njes Aj), if k is even SC1,2,...,n||S|=l
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