MHB How to Calculate Poisson Distribution Probabilities?

AI Thread Summary
To calculate Poisson distribution probabilities, identify the mean rate of occurrence, λ, which is 25 disintegrations per minute in this case. Convert the time frame from minutes to seconds, yielding a λ of 5 for 12 seconds. The probability mass function is used to find the probabilities for specific counts, where P[X=k] = (λ^k * e^(-λ)) / k!. For this scenario, the calculations involve determining P[X=0] for no disintegrations and P[X>2] for more than two disintegrations. Understanding these fundamentals allows for accurate probability assessments within the Poisson framework.
mathsforumuser
Messages
1
Reaction score
0
Hi guys I got a question on the poisson distribution and never previously done stats at all.

It follows:

The mean count of a radioactive substance is 25 disintegrations per minute. Using the Poisson distribution, find the probability that, in a time of 12 seconds, there are-

i) No disintegrations

ii) More than 2 disintegrations
 
Physics news on Phys.org
Hi mathsforumuser,

Welcome to MHB! :)

When working with any discrete probability distribution, we often need to use the probability mass function. For a Poisson distribution this is:

$$P[X=k]=\frac{\lambda^k e^{-\lambda}}{k!}$$

For this problem, what is $\lambda$? What is $k$?
 
Back
Top