# Math Help - Conditional Poisson!

1. ## 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

2. Originally Posted by Dogod11
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

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

I do not understand your last sentence.

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5. Originally Posted by Dogod11
Sorry, but understand that $P(U)$ is likely to be measuring uranium.

I do not understand your last sentence.

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

CB