Session 2: Probability distributions and density functions

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Session2: p. :Probabilitydistributionsanddensityfunct ions p. :Probabilitydistributionsanddensityfunct ions p. 3RandomvariablesSession2:Probabilitydist ributionsanddensityfunctions p. 4RandomVariablesA randomvariableis ,thevalueofthefirstrollofa ,thesumofa rolloftwo ,therollofa dice,ortheoutcomeofahorserace, ,thenumberofwhitehaironmyhead,orhow muchdividendINFOSYSTCHwillannouncenextye ar, :ContinuousRVscanhave a fixedminimumormaximum,however, :Probabilitydistributionsanddensityfunct ions p. 5ProbabilitydistributionsSession2:Probab ilitydistributionsanddensityfunctions p. 6Whatis a probabilitydistribution?Fora discreteRV, theprobabilitydistribution(PD)isa ,intherollofa die:ValueProbabilityValueProbability11/6 41/621/651/631/661/6A probabilitydistributionwillcontainallthe outcomesandtheirrelatedprobabilities, :Probabilitydistributionsanddensityfunct ions p. 7Howtoreada probabilitydistribu-tionFromthedistribut ion,wecanfind:X = 3Pr(X= 3) = 1=6X = evennumberPr(X= 2orX= 4orX= 6) = 3=6 = 1=2Moreinteresting,wecanalsofind:Pr(X >3) = 3=6 = 1=2Thisis calledacumulative :Probabilitydistributionsanddensityfunct ions p.

The aim of this session 1. Discrete and continuous random variables 2. Probability distributions 3. Case 1: The bernoulli distribution 4. Case 2: The binomial distribution

  Distribution, Functions, Probability, Density, Bernoulli, Probability distributions and density functions