extraprobs1

# extraprobs1 - and not a constant show it must be...

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More Problems #1 1.

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4.

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5. 6. For the situation in #5 suppose the sum of the probabilities of the A's is finite. Show P(Y=oo) = 0 . On the other hand, if the A's are independent and the sum is oo show P(Y=oo) =1 . These two results form the Borel Cantelli Lemma. 7. 8. 9. A positive rv X is ageless if P(X>s+t|X>s)=P(X>t) , for all s,t>=0 . If X is ageless,

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Unformatted text preview: and not a constant , show it must be exponential(l) for some l>0. Remark : In 9 you may not assume X to be a cts rv with some pdf. If F is the df then you must show 1-F(x)=exp(-lx) for x>0 . Since 1-F is right continuous this will be the case if it's true for rational x's ....
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