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Math Help - Problem of Poisson Process

  1. #1
    kin
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    Problem of Poisson Process



    i can solve only the first two questions... anyone help me the rest, hints please...
    Last edited by kin; July 14th 2010 at 11:35 PM.
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  2. #2
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    Quote Originally Posted by kin View Post


    i can solve only the first two questions... anyone help me the rest, hints please...


    (a) Determine the expected amount of time between loss occurrences.

    E( amount of time between loss occurrences) = 1/ (1/10 +1/25 +1/5)=2.94

    (b) What is the chance of the first theft loss occurring prior to a wind loss?

    the chance=P(time of 1st theft loss < time of 1st wind loss)expotentiallydisributed,
    = (1/25) / ( 1/10 + 1/25)
    = 0.2857


    (c) What is the chance that the fifth loss is an earthquake loss?
    (d) What is the chance that the fifth loss has occurred by time t = 11.76 years?
    (e) The 9th loss is observed at time 31.62, what is the chance that the 3rd loss occurred
    before time t = 8 years?
    (f) Exactly 3 losses are observed, one of each type, prior to time t = 8 years, what is
    the chance that the earthquake loss occurred before time t = 5 years?
    (g) The 4th loss is a theft loss which occurs at time t = 9.2 years. The first three losses
    included exactly one wind loss. What is the chance that the wind loss occurred
    before time t = 2.7 years?
    (h) What is the chance that is it more than 4 years between the 7th and 8th loss?
    (i) What is the chance of observing 4 wind losses before observing 6 theft losses?
    (j) What is the chance of both the 5th and 10th losses being from earthquakes?
    (k) What is the chance that the 4th loss is a wind loss of size greater than $1000?
    (l) What is the expected time between earthquakes of size greater than $1000?
    (m) What is the expected waiting time until the first theft loss of size greater than
    $1000?
    (n) A loss of size greater than $1000 is observed, what is the chance that the loss is an
    earthquake?
    (o) What is the expected waiting time until the first loss of size greater than $1000 is
    observed?
    (p) What is the chance there has been at least four theft losses, at least three wind
    losses and at least two earthquake losses by time t = 20 years?
    (q) What is the chance of the 4th loss being a theft and the 7th loss being from wind?
    Sorry but this question has way too many parts. In fact, it reads like an assignment question, in which case it should be noted that MHF policy is to not knowingly help with work that counts towards a student's final grade. It's meant to be the student's own work.

    Thread closed. You can discuss this with me via pm if you want. But regardless, there are way too many parts to the question.

    Edit: Re-opened (reluctantly) after getting a pm which contained, in part, what I have posted in the next post.
    Last edited by mr fantastic; July 13th 2010 at 04:59 AM.
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  3. #3
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    Written by kin in a pm:

    ------------------------------------------------------------------------------------------------
    [The posted] question is from one of my past exam papers,

    have i got the first 2 questions right?

    u dont have to explain all of them , coz some of them are similar.

    let's discuss (c)(d)(e):
    (c) no idea

    (d)let N(t) be the no.of loss,
    so, the required probability
    = P( N(11.76) >= 5) since there must be 5 loss before t=11.76
    = summation( j=5 to ∞) [ (exp-λt)((λt)^j) / (j!) ] -->it's possion(λt)
    =1 - summation( j=0 to 4) [ (exp-λt)((λt)^j) / (j!) ]

    where λt is the possion rate , from part(a)
    λ= 1/10 + 1/25 + 1/5 =0.34 , λt=(0.34)(5)= 1.7
    (e)
    the required probability
    = P ( N(8)>=3 |N(31.62)>=9)
    =P(N(8)>=3) since the possion increment is independent
    =1 - summation( j=0 to 2) [ (exp-λt)((λt)^j) / (j!) ]

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