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Bernoulli Distribution - University of Chicago

BernoulliDistributionExample:Tossof coinDe neX= 1 if headcomesupandX= 0 if : (X= 1) = (X= 0) =12 Examples:Often:Two outcomeswhich arenotequallylikely: Successof medicaltreatment Interviewed personis female Student passesexam Transmittanceof a diseaseBernoullidistribution(withparamet er ) Xtakes two values,0 and1, withprobabilitiespand1 p FrequencyfunctionofXp(x) = x(1 )1 xforx2f0;1g0otherwise Often:X= 1if eventAhasoccured0otherwiseExample:A= blood pressureabove 140 , Jan 30, 2003- 1 -BernoulliDistributionLetX1; : : : ; Xnbe independent Bernoullirandomvariableswithsameparamete r.

Classical example from von Bortkiewicz (1898). – Number of fatalities resulting from being kicked by a horse – 200 observations (10 corps over a period of 20 years) Statistical model: – Each soldier is kicked to death by a horse with probability µ. – Let Y be the number of such fatalities in one corps. Then Y » Bin(n;µ)

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