100922u - AGENDA Gamma distribution Exponential...

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Sheet1 Page 1 AGENDA Gamma distribution Exponential distribution Beta distribution Weibull distribution Exam review Optional Homework Quiz GAMMA DISTRIBUTION GAMMA DISTRIBUTION GAMMA DISTRIBUTION EXPONENTIAL DISTRIBUTION Gamma distribution with alpha parameter=1 Related to random poisson processes Poisson distribution was number of observations in a given period of time Exponential distribution is the time between observations for a poisson process EXPONENTIAL DISTRIBUTION EXPONENTIAL DISTRIBUTION EXPONENTIAL DISTRIBUTION The exponential distribution function can be integrated and evaluated to obtain cumulative distribution function values EXAMPLE Trucks arrive randomly to a warehouse at an average rate of 3 per hour What is the probability that the interarrival time between trucks will be Less than 5 minutes? At least 45 minutes? EXAMPLE Solution Integrate the probability function using e^u du substitution F(x)=1-e^-(x/B) 3 per hour ---> B = 1/3 hour between arrivals Evaluate between 0 and 1/12 hour 1-e^(-(1/12)/(1/3)) 1-e^(-1/4)=0.221 Evaluate between 3/4 and infinity 1-(1-e^(-(3/4)/(1/3))) e^(-9/4)=0.105 BETA DISTRIBUTION Continuous random variable that is between 0 and 1 Frequently used in engineering project management
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Sheet1 Page 2 Probability that some task will be completed on time Parkinson} s law Student syndrome Parameters Alpha Beta BETA DISTRIBUTION BETA DISTRIBUTION WEIBULL DISTRIBUTION
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100922u - AGENDA Gamma distribution Exponential...

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