Some Example Applications of Distribution Functions Jake Blanchard Spring 2010 Uncertainty Analysis for Engineers1

Poisson Lightning strikes – in any small time interval, there is a certain probability that a strike will occur Discontinuities in continuous manufacture of wire (measure is length of wire) Consumption of bacteria from lake – (measure is volume of water consumed) Company insures planes-crash rate is 0.23 crashes/month – what is distribution of costs? Uncertainty Analysis for Engineers2

Poisson Rain 270 drops/s/m2 – each drop is 1 ml – barrel is 1 m high and R=0.3 m – How long to fill? Uncertainty Analysis for Engineers3

Binomial Coin tosses Two experts guess age of 20 wines ◦ A gets 11 right ◦ B gets 14 right ◦ What is confidence that B is “better” than A Multiple choice tests ◦ 50 questions, 3 possible answers each ◦ A gets 21/50 ◦ What is probability that guessing would have done as well? Uncertainty Analysis for Engineers4

Binomial Darts – I get “double top” 1/20 times – how many will I get in 10 throws Uncertainty Analysis for Engineers5

Hypergeometric Population survey Herd testing Lotto Pick 10 names from 2 bags – A contains 15 men and 22 women – B contains 12 men and 15 women – What is probability of having same ratio of men to women in two picks How many cards must we turn to get a heart? Uncertainty Analysis for Engineers6

Hypergeometric Post office is considering opening another service counter – people arrive at 1/12 minutes – time to serve is lognormal – What is max queue size? Estimate of animal population – catch, tag, and release animals – then catch some more and count tagged animals Uncertainty Analysis for Engineers7

Exponential Circuit has constant failure rate – circuit lasts average of 5200 hours Uncertainty Analysis for Engineers8

Extreme Value (Gamma) Town floods every 6 years – how many years to get 4 floods Uncertainty Analysis for Engineers9

Lognormal Estimate particle size of aggregate Incubation period of infectious disease Uncertainty Analysis for Engineers10

Uniform Angular resting position of camshaft after spinning Wait time for bus Distance of leak in pipe network to nearest joint Uncertainty Analysis for Engineers11

Poisson Frequency of deaths in Prussian army Uncertainty Analysis for Engineers12