Answered: a) IA1-IA; b) IAB = IAIB; c) For any…

a) IA1-IA; b) IAB = IAIB; c) For any collection of events A₁,… An, the indicator of their union is IUA, 1-(1-IA₁)(1 — IA₂) · (1 – IA₂).

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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Question

Let I_A be the indicator of an event A. Show the following identities:

a) IA=1-IA;
b) IAB = IAIB;
c) For any collection of events A₁," An, the indicator of their union is
IUA; = 1 − (1 — IA₁)(1 — IA₂) ··· (1 — IA„).
d) Expand the product in the last formula and use the rules of expectation to derive the
inclusion-exclusion formula.

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