Physics307L:Schedule/Week 10 agenda/Poisson

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Poisson Distribution

p(k;\lambda)=\frac{\lambda^k e^{-\lambda}}{k!},\,\! (This is a probability mass function)

Is the limit of the bionomial distribution when probability of success goes to zero, number of trials goes to infinity, and p*n = lambda

\ \sigma_{k}\, =\, \sqrt{\lambda}

For a given collection of data, thought to be Poisson distributed, the maximum likelihood fit is

\lambda = \frac {\sum{x_i}}{N},

where x_i are the counts recorded in each trial, and N is the number of trials

Example: decay of radioactive sample

p_\mathrm{Poisson}(k;\lambda) \approx p_\mathrm{normal}(k;\mu=\lambda,\sigma^2=\lambda)\,
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