Question

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Let T1, T2, T3, and T4 be four independent events.

a) Provided that P(T3) > 0, show that T4 and T2 are conditionally independent given T3?

b) Provided that P(T3 ∩ T4) > 0, prove that P(T1 ∪ T2 | T3 ∩ T4) = P(T1 ∪ T2)

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Given T1, T2, T3 and T4 are independent events.

(a) Given, P(T3)>0

We have to prove that P(T4|T3)= P(T4) and also P(T2|T3)= P(T2)

( since T4 and T3 are independent.)

Here we proved that T4 and T2 are conditionally independent given T3.

(b) Given, , we have to prove that

P(T1 ∪ T2 | T3 ∩ T4) = P(T1 ∪ T2)

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