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Problem 1.10: Let P1 and P2 be two probability functions on Ω. Defne a new function...

Problem 1.10: Let P1 and P2 be two probability functions on Ω. Defne a new function P such that P(A) = (P1(A) + P2(A))/2. Show that P is a probability function.

Math   Statistics-And-Probability   
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Answer #1

Given, P1 and P2 are two probability functions on .

Then, for any set A on ,

  & and

&

Define , function such that

Then,

&

and

Hence, is a probability function. Proved

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