Poisson Distribution

Apr 2010
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An individual suffers from a particular disease which leads to him having attacks from time to time. The number of attacks per month can be assumed to follow a Poisson distribution with mean 2. He is included in a trial for a new treatment. In the trial there is a 50% probability that he will recieve a placebo treatment which will not affect the rate of attacks and a 50% probability that he will recieve the new treatment which should reduce the mean number of attacks per month to one. In the first month of the trial, he has no attacks.
Calculate the probablity that he has recieved the new treatment.

This is an exam question from a past paper and a question of this format will probably come up this year so some guidance of how to tackle these types would be very useful.

Thank you
 

mr fantastic

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An individual suffers from a particular disease which leads to him having attacks from time to time. The number of attacks per month can be assumed to follow a Poisson distribution with mean 2. He is included in a trial for a new treatment. In the trial there is a 50% probability that he will recieve a placebo treatment which will not affect the rate of attacks and a 50% probability that he will recieve the new treatment which should reduce the mean number of attacks per month to one. In the first month of the trial, he has no attacks.
Calculate the probablity that he has recieved the new treatment.

This is an exam question from a past paper and a question of this format will probably come up this year so some guidance of how to tackle these types would be very useful.

Thank you
Let X be the random variable 'number of attacks during placebo treatment'.

Let Y be the random variable 'number of attacks during new treatment'.

A tree diagram will now make the following clear:

Pr(new treatment | number of attacks = 0) = A/B where A = 0.5 Pr(Y = 0) and B = 0.5 Pr(Y = 0) + 0.5 Pr(X = 0).