Result classroom assessment / Uncertainty Modelling M. H. Faber. Yovisto Academic Video Search. Poisson counting process, Continuous random processes,Stationarity and ergodicity random variable SEQUENCES probability uncertainty today process Poisson load distribution counting probabilit Marginal Joint Exponential Eidgenössische Technische Hochschule Zürich (ETHZ) technology institut federal swiss calculated probability corresponding inter event sequenc then landfall typhoon denot distribution geometric technology institut federal swiss independent event assum mak first sequenc what island landfall mak typhoon that probability distribution geometric technology institut federal swiss function density probability gamma sequenc technology institut federal swiss variabl random result repeated from this distribution gamma follows then tim waiting distributed exponentially independent crossing roadway car arrival repair modeling engineering inter event till tim sometim sequenc technology institut federal swiss variabl distributed exponentially varianc valu expected accident traffic earthquak next failur till tim tim waiting modeling applied frequently distribution exponential sequenc random exponential sequenc technology institut federal swiss function distribution cumulativ density probability technology institut federal swiss exponential equal that recognizing derived easily event first till tim waiting function distribution probability sequenc technology institut federal swiss achieved directly this year next earthquak structur failur year storm sev problem engineering inter special oft interval tim giv event probability distribution exponential sequenc technology institut federal swiss cas interval tim giv event numb describing variabl random varianc valu mean technology institut federal swiss raid london und hit distribution study clark guinness production beer testing sampl small student gosset sealy william suicid child cavalry prussian death kick hors bortkiewicz ladislaus studi includ application early sequenc technology institut federal swiss interval tim event probability inhomogeneous otherwis homogeneous said constant event intensity completely described process poisson sequenc mor proportional asymptotically event fulfilled condition following called interval tim event numb denoting prccess theory reliability distribution probability famili applied commonly most process counting poisson sequenc random technology institut federal swiss independent mutually interval disjoint ord high function than technology institut federal swiss tim over numb event rar representing model provid theory reliability distribution probability famili applied commonly most process counting poisson sequenc technology institut federal swiss procedur improvement theory probability applying interested clerk form laplac student simeon-denis boy teach mathematics thing good only lif invented originally process counting poisson sequenc technology institut federal swiss technology institut federal swiss total nail rain fain fail probability marginal technology institut federal swiss nail rain condition health what probability marginal distribution gamma exponential event betwe tim waiting process poisson sequenc random look summary today doing technology institut federal swiss retum severity certain exceeding event occurrenc till expected extrem period referenc within valu maximum ergodicity stationarity extrem extrapolation criteria normal process continuous load wav technology institut federal swiss period return severity certain exceeding event occurrenc till tim expected distribution referenc giv quantity uncertain valu maximum event modeling interested howev level wat extrem today doing technology institut federal swiss normal process temperatur land wav pressur wind continuously variatian ring valu stress continuous distribution gamma exponential process poisson queu earthqua rock-fall tim point event occurrenc tam flood event discret random describ abl need problem engineering many today doing technology institut federal swiss period referenc giv observed variation data statistical knowledg lack model tim vary represent oft observation based quantify which uncertainti representing mean variabl random introduced already hav today doing thus load truck maximum flood storm earthquak design year exceeding futur happ might account into tak need making decision problem real many experienc from fram tim related observation based quantify which uncertainti representing mean variabl random introduced already hav today doing technology institut federal swiss phenomena uncertain extrem modeling support model develop technology institut federal swiss making event modd duta phenom uncertain modeling uncertainty context decision technology institut federal swiss modeling uncertainty context decision technology institut federal swiss equal thus must beam height function failur probability calculating variabl random technology institut federal swiss function distribution cumulativ standard from determined easily failur probability varianc equal valu expected variabl distributed normal combination linear that learned already hav variabl random technology institut federal swiss equal probability annual determin furth margin safety called this failur event writ 20kn giv stress yield load that assum variabl random equal lur probability annual determin 5000mm furth failur event writ giv stress yield load that assum tech fad technology institut federal swiss equal probability annual determin furth margin safety called this failur event writ 20kn giv stress yield load that assum variabl random technology institut federal swiss safety requirement numb giv equal less failur that designed beam probability howev choic independent certainty with fulfilled cannot equation design uncertain stress yield load variabl random technology institut federal swiss unknown produced stress yield steel year period during load variability represent gain distributed normal variabl equation design representing accounted uncertainty variabl random till technology institut federal swiss unknown produced stress yield steel year period during load variability represent distributed normal variabl equation design representing accounted uncertainty variabl random with associated that rath select must engine equation design establish variabl random technology institut federal swiss account into this mak uncertainty beam length load technology institut federal swiss steel ofth stress section calculated span cross-section capacity moment variabl random technology institut federal swiss uncertainty with associated stress yield section cross resistanc being moment bending midspan effect load controlling that experienc based assum beam steel design want probl engineering structural simpl very consid variabl random technology institut federal swiss total rain conditional probability joint jail bill fail technology institut federal swiss rain conditional probability joint technology institut federal swiss health condition weath what und run when get rain rain that sola attend supposed professor conditional probability joint technology institut federal swiss measur dispersion event spac sampl theory prob bask representation graphical variabl random jaunt technology institut federal swiss mail bpag federal swiss follow detail today doing context decision variabl random what assessment classroom result presentation lectur todays content technology institut switzerland zurich technology institut federal swiss fab michael prof engineering environmental surveying civil theory probability statistics