Problems on life testingLet X1,â?¦..,Xnbe independent distributed with exponential density (2?)-1e-x

Problems on life testingLet X1,…..,Xnbe independent distributed with exponential density (2?)-1e-x/2?for x>, and let the ordered X’s be denoted by Y1<><><><><=yrandfind the=”” mle=”” of=”” (maximum=”” likelihood=”” estimator=”” of=”” 2?the=”” distribution=”” of=”” [?ri=”1Yi+(n-r)Yr]/?” is=”” with=”” 2r=”” degrees=”” of=”” freedom3?let=”” y1,y2,……..denote=”” the=”” time=”” required=”” until=”” the=”” first,=”” second,……event=”” occurs=”” in=”” a=”” poisson=”” process=”” with=”” parameter=”” 1/2?’,=”” then=”” z1=”Y1/?’,” =(?2-?1)/?’,=”” =(?3-?2)/?’,…….are=”” independent=”” distributed=”” as=”” with=”” 2=”” degrees=”” of=”” freedom,and=”” the=”” joint=”” density=”” of=”” y1,……,yris=”” an=”” exponential=”” family=”” with=”” density[1/(2?’)r]exp(-yr/2?’),=””>=yrandfind><><><=yr .=”” the=”” distribution=”” of=”” yr/?’=”” is=”” again=”” with=”” 2r=”” degrees=”” of=”” freedom.4?the=”” same=”” model=”” arises=”” in=”” the=”” application=”” to=”” life=”” testing=”” if=”” the=”” number=”” n=”” of=”” tubes=”” is=”” held=”” constant=”” by=”” replacing=”” each=”” burned-out=”” tube=”” with=”” a=”” new=”” one,=”” and=”” if=”” y1denotes=”” the=”” time=”” at=”” which=”” the=”” 1st=”” tube=”” burns=”” out,=”” y2the=”” time=”” at=”” which=”” the=”” 2nd=”” tube=”” burns=”” out,=”” and=”” so=”” on,=”” measured=”” from=”” some=”” fixed=”” time.=”” the=”” lifetimes=”” are=”” assumed=”” to=”” be=”” exponentially=”” distributed.=””>=yr>