6. Show that if A1, A2, ... is an expanding sequence of events, that is, AC...

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Question

math Statistics-And-Probability

Answer 1

Answer #1

It is given that A1, A2, ... is an expanding sequence of events, i.e. A1 is contained in A2, A2 is contained in A3, and so on.

Therefore, P(A1 U A2 ) = P( A2 )

P( A2 U A3 ) = P( A3 )

Therefore, P( A1 U A2 U A3 ) = P( A3 )

Then for n number of events, P( A1 U A2 U .... ) = lim n --> inf P( An ), provided the limit exists.

Answer 2

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