3719, 2039, 2272 2061 Email: [email protected] Email: corp ...
Lecture 7: Poisson Distribution - Astronomybelz/phys3719/lecture07.pdf2 February 2011 Physics 3719...
30
Lecture 7: Poisson Distribution Physics 3719 Spring Semester 2011 Simon Denis Poisson (1781-1840)
Transcript of Lecture 7: Poisson Distribution - Astronomybelz/phys3719/lecture07.pdf2 February 2011 Physics 3719...
Lecture 7: Poisson Distribution
Physics 3719Spring Semester 2011
Simon Denis Poisson(1781-1840)
2 February 2011 Physics 3719 Lecture 7
Review: Experimental and Parent Distributions
● Measure: experimental
● Infer: parent
● Physics is in the parent distribution
● Probability distribution: Normalized probability of finding event in a given bin.
2 February 2011 Physics 3719 Lecture 7
The 3 (most?) Important Probability Distributions
● Binomial: Result of experiment can be described as the yes/no or success/failure outcome of a trial. The probability of obtaining success is known.
● Poisson: Predicts outcome of “counting experiments” where the expected number of counts is small. (Special case of binomial.)
● Gaussian: Predicts outcome of “counting experiments” where the expected number of counts is large. (Special case of binomial.)
2 February 2011 Physics 3719 Lecture 7
Important Distributions
● Binomial
2 February 2011 Physics 3719 Lecture 7
Discussion
● Can radioactivity counting experiment be treated as a binomial distribution problem?
● What are some practical difficulties one might encounter in doing so?
2 February 2011 Physics 3719 Lecture 7
Poisson Distribution
2 February 2011 Physics 3719 Lecture 7
Binomial Distribution
Poisson Distribution
2 February 2011 Physics 3719 Lecture 7
2 February 2011 Physics 3719 Lecture 7
Example of Poisson Distribution
● Poisson distributed data can take on discrete integer values.
● n must be an integer
● need not be!
2 February 2011 Physics 3719 Lecture 7
Example: Suppose there are 30,000 University of Utah students of which 400 carry concealed weapons permits. If JB is teaching an astronomy class of 120 students, what is the probability that one or more is packing?
2 February 2011 Physics 3719 Lecture 7
Example: Counting Experiments (Lab #2)
2 February 2011 Physics 3719 Lecture 7
Explain: Using a Geiger counter, I measure the activity of a weakly radioactive rock. I record a small number (<5) counts in a ten second interval.
Why do I expect the number of counts I'd measure in repeated trials to be Poisson Distributed?
2 February 2011 Physics 3719 Lecture 7
Example: The background radiation rate as measured in a particular room with a particular Geiger counter is known to be 1800 counts per hour.
a) If I run the Geiger counter in the room for a five second interval, how many counts do I expect to see?b) What is my uncertainty for the number of expected counts in five seconds? c) What is the probability of measuring 0 counts in 5 seconds? 1 count? 2 or more counts?
2 February 2011 Physics 3719 Lecture 7
Example: The background radiation rate as measured in a particular room with a particular Geiger counter is known to be 1800 counts per hour.
a) If I run the counter for 100 1-second long trials, how many trials do I expect to result in zero counts? b) What is the uncertainty in the number of zero count trials?
2 February 2011 Physics 3719 Lecture 7
Example: Assuming negligible uncertainty in timing, how many counts are required to measure a rate with 0.1% precision?
2 February 2011 Physics 3719 Lecture 7
Example: Now, suppose your timer has a random uncertainty of 0.05%. In this case, how many counts are required to measure a rate with 0.1% precision?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
What Happens as Becomes Large?
2 February 2011 Physics 3719 Lecture 7
Binomial Distribution
Poisson Distribution
Gaussian (Normal)Distribution
2 February 2011 Physics 3719 Lecture 7
2 February 2011 Physics 3719 Lecture 7
Additional Reading and Problems
● Read in Taylor: – Ch 5: The Normal
Distribution (Sections 1 and 2)
– Chapter 10: The Binomial Distribution
– Ch 11: The Poisson Distribution
● Try the problems:– 5.4, 5.6, 5.12– 10.9, 10.10, 10.11,
10.20, 10.21, 10.22– 11.1, 11.3, 11.8,
11.10, 11.14, 11.18, 11.20
![Measurement of Planck’s constant, h - Astronomybelz/phys3719/presentations/peterson.pdfPlanck’s Constant •Describes the size of quanta [2] •Most prevalent constant along with](https://static.fdocuments.us/doc/165x107/5ab84d4b7f8b9ad3038ca416/measurement-of-plancks-constant-h-belzphys3719presentationspetersonpdfplancks.jpg)
