Poisson Distribution
Learning Objectives
- Derive the poisson distribution
- Compute the statistical moments
- Interpret the meaning of the moments with respect to radioactive decay
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Overview
A radioactive isotope decays with a unique, characteristic time. This is conceptualzied by a stochastic process. That is, the exact time any particular atom decays cannon be known. Therefore, a probablilty distribution is used to describe the behavior of radioactive decay.
Poisson distribution
The statistical distribution applied to describe decay is the Poisson distribution. If the average number of decays in a period of time is defined as
where $\lambda$ is defined as the decay constant, specific to the radioactive isotope, then the probablity of an exact number of $n$ decays that will occur in $\Delta t$ is:
Assessments
Overview
A radioactive isotope decays with a unique, characteristic time. This is conceptualzied by a stochastic process. That is, the exact time any particular atom decays cannon be known. Therefore, a probablilty distribution is used to describe the behavior of radioactive decay.
Poisson distribution
The statistical distribution applied to describe decay is the Poisson distribution. If the average number of decays in a period of time is defined as
where $\lambda$ is defined as the decay constant, specific to the radioactive isotope, then the probablity of an exact number of $n$ decays that will occur in $\Delta t$ is: