Poisson Distribution Question w/ one variable

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In a physics experiment, a photographic plate is placed in front of a beam of radioactive particles, When a particle hits a plate, it leaves a trace on the plate. The number of such traces on a plate at the end of the experiment has a Poisson distribution. After a long series of experiments under similar conditions, the probability of a completely blank plate (no traces) was found to be 0.07.What should be the most frequently occurring number of traces? (Hint I am not asking for the mean here)

Apr 25th, 2015

We have to find first the parameter lambda which defines the distribution.

Poisson dist (lambda, k)=lambda^k*e^(-lambda)/k!

we have Poisson (lambda,0) = 0.07

using 0!=1, we get:

e^(-lambda)=0.07

taking natural logs of both sides:

lambda = -ln(0.07) = 2.659  (I used the LN function in Excel)

The poissn distribution is only defined for natural numbers and 0. the peak is is usually near natural numbers close to lambda and there is only one peak. We can use the poisson function is Excel to calculate for n=0, 1, 2:

to find:

Poisson (2.659, 0)=0.1861

Poisson (2.659, 1)=0.2475

Poisson (2.659, 2)=0.2194

Thus the most frequent occurrence of such events is 1

Apr 25th, 2015

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Apr 25th, 2015
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Apr 25th, 2015
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