Let be a sample space and suppose we have defined a set function, P(), which satisfies

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Let Ω be a sample space and suppose we have defined a set function, P(⋅), which satisfies the properties P1–P3 of Definition 1.10, on that space. Examine whether each of the set functions defined below can be used as a probability on that space;

here, A is an arbitrary event on Ω.

(i) P1(A) = P(A)∕2 (ii) P2(A) = 1 − P(A)

(iii) P3(A) = |P(A)| (iv) P4(A) = [P(A)]2

(v) P5(A) = (P(A) + 1)∕2 (vi)P6(A) = (1 − P(A))∕2.

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Introduction To Probability Volume 2

ISBN: 9781118123331

1st Edition

Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis

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