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Math Help - Conditional Poisson!

  1. #1
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    Conditional Poisson!

    Hello,
    By measuring pulses of uranium with a Geiger counter, those arriving to a rate of 2 per second. Measuring Plutonium, the arrival rate is 5 per second. Si durante dos segundos no se producen arrivos,

    For two seconds if there are no arrivals,

    What is the probability that uranium had been measuring?

    I hope you or someone can help me, I still think that a conditional Poisson distribution is Erlang, but I'm not sure.

    A greeting and thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Dogod11 View Post
    Hello,
    By measuring pulses of uranium with a Geiger counter, those arriving to a rate of 2 per second. Measuring Plutonium, the arrival rate is 5 per second. Si durante dos segundos no se producen arrivos,

    For two seconds if there are no arrivals,

    What is the probability that uranium had been measuring?

    I hope you or someone can help me, I still think that a conditional Poisson distribution is Erlang, but I'm not sure.

    A greeting and thanks
    Bayes' theorem tells you that:

    P(U|2s)=\frac{P(2s|U)P(U)}{P(2s)}=\frac{P(2s|U)P(U  )}{P(2s|U)P(U)+P(2s|Pu)P(Pu)}

    where 2s denotes no detections for two seconds.

    You can calculate P(2s|U) and P(2s|Pu) from the given rates and the Poisson distribution.

    P(U) and P(Pu) are the probabilities that each sample is choosen and I expect these are supposed to both be 0.5.

    CB
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  3. #3
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    Thank CaptainBlack's, I know and know how to work with the definition of conditional probability but does not know why I was messing,


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  4. #4
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    Sorry, but understand that P(U) is likely to be measuring uranium.

    I do not understand your last sentence.

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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Dogod11 View Post
    Sorry, but understand that P(U) is likely to be measuring uranium.

    I do not understand your last sentence.

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    You are not told the probability that U is chosen and we have to assume P(Pu)=1-P(U)

    CB
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