3 - Important Probability Distributions in Physics Binomial...

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1 Important Probability Distributions in Physics • Binomial Distribution – Generally applies to experiments in which the result can be one of only a small number of possible outcomes/final states • Poisson Distribution – Generally applies to ‘counting’ experiments • Exponential Distribution – Describes the time between ‘counts’ in a Poisson Process. A ‘memoryless’ distribution function (this will be explained) • Normal/Gaussian Distribution – Enormous breadth of applicability. In certain limits (described by the Central-limit theorem) most other distributions converge to a Normal distribution. Permutations and Combinations )! ( ! ) 1 )( 2 ( ) 2 )( 1 ( ) , ( x n n x n x n n n n x n Pm = + + = L ! ) 1 ( ) 2 )( 1 ( ) , ( n n n n n n Pm = = L How many permutations are there for ‘x’ objects selected from a set/group of ‘n’ distinct objects: How many different ways are there to arrange ‘n’ distinct objects? (Each distinct arrangement is called a ‘permutation’, Pm) How many of these permutations (i.e. Pm(n,x) ) result in the same combination of ‘x’ objects being selected (i.e. where the order in which they are selected is not important) :
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3 - Important Probability Distributions in Physics Binomial...

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