Let (Ω, F, P) be a probability space and let A, B, C be events with P(C) > 0. We call A and B (conditional) independent given C if and only if P(A ∩ B|C) = P(A|C)P(B|C). (a) Show that conditional independence can be understood as independence with respect to a suitably chosen probability measure P˜ on (Ω, F). (b) There are two coins in a box. One coin is a fair coin, the other coin is a fake coin with a head on both sides. We blindly take a coin from the box and toss it. Then we throw it remaining coin. We watch the events A = 'the first coin lands heads'; B = 'the second coin lands heads';

Let (Ω, F, P) be a probability space and let A, B, C be events with P(C) > 0. We call A and B (conditional) independent given C if and only if P(A ∩ B|C) = P(A|C)P(B|C). (a) Show that conditional independence can be understood as independence with respect to a suitably chosen probability measure P˜ on (Ω, F). (b) There are two coins in a box. One coin is a fair coin, the other coin is a fake coin with a head on both sides. We blindly take a coin from the box and toss it. Then we throw it remaining coin. We watch the events A = 'the first coin lands heads'; B = 'the second coin lands heads';

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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