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Thread: Is there a trick to this problem?

  1. #11
    Actuary.com - Level V Poster
    Join Date
    Jan 2006
    Quote Originally Posted by Deltad View Post
    Oh man... are you kidding me? lol... will this work for all exponential function? can anyone prove this?
    anyway, the "trick" doesn't make sense to me... it would make more sense if it was 7/(6+7) since you want the probability that the Deluxe happens first.

    I didn't get to order statistic since my friend who passed the test already said it wont be on exam P, I can see that it'll help though.

    Thank you ctperng!
    You are welcome!

    But the information from your friend is incorrect. Order statistic in on the syllabus: See

    (part 3. item transformations and order statistics)

    The previous trick works for expenential distributions as can be seen from my two proofs, either using order statistics or by direct integrations.

    This makes sense, because if the mean is higher, the probability of first occurence should be lower. Of course, if I have time I can also show a different way of looking at this phenomenon.

    Anyway, good luck on your study!


  2. #12
    Actuary.com - Newbie Poster
    Join Date
    Jan 2017
    The first time I tried this problem I tried doing P(D<B), or P(D-B>0). I then calculated E(D-B)=3-2=1. The variance is sqrt(3^2+2^2)=sqrt(13).
    I then did (0-1)/sqrt(13)=-.277, which returns a probability of .3936. What is the reason that normal approximation doesn't work here? Is it because there is nothing that says that there are at least 30 independent claims?

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