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Poisson statistics : Measurement of gamma radiation from 137 Cs source

Tony Hyun Kim 9/26/2008 8.13 MW2-5. Poisson statistics : Measurement of gamma radiation from 137 Cs source. Topics to be discussed. Probability theory Independent events Poisson distribution Experimental setup Results Comparison to Matlab-generated Poisson data sets

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Poisson statistics : Measurement of gamma radiation from 137 Cs source

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  1. Tony Hyun Kim 9/26/2008 8.13 MW2-5 Poisson statistics: Measurement of gamma radiation from 137Cs source

  2. Topics to be discussed • Probability theory • Independent events • Poisson distribution • Experimental setup • Results • Comparison to Matlab-generated Poisson data sets • Discussion of errors • Conclusions

  3. Independent events • Occurrence of one event does not affect the likelihood of others. • Radioactive emission of photons by sample of 137Cs

  4. Poisson distribution • A process involving independent events with “mean rate”: λ • Observation period: T • Expected number of events (“on average”): μ = λT

  5. Experimental details • Main “knobs”: • Source-detector distance • Amplifier gain • Configured for counting rates of 1, 4, 10, 100 sec-1 • Took 100 one-second measurements.

  6. What is the characteristic of the parent distribution? • The long 100-s measurement yields: λ = 87.5 sec-1 • Confirmed by cumulative averages of 1-second data Final assessment of mean:

  7. Matlab generated Poisson sets • Measured data set is characterized by: • Reasonable? Given parent Poisson distr: • Generated 100-element Poisson data sets, to find statistical fluctuations on

  8. Does Poisson fit? • Is of the measured set typical? • Measured set: • Simulated set: • Does ? • Measured set: • Simulated set:

  9. Brief error analysis • Our expt. and analysis are robust against “hidden sources” Other sources

  10. Conclusions • Counting experiments of emission from Cs. • Direct fit shows that Poisson distr. describes data well. • Comparison with Matlab-generated sets show: • Data set parameters within statistical fluctuations • The relation holds for data

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