Need all 15 questions completed with detailed work and some explanation. These questions cover stochastic process, distributions, random variables, joint densities, and general probability.
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QUESTIONS
QUESTIONS 22 1) Consider a stochastic process ()cos( 1)sin, and are independent random variables wi th ()()0, ()()1. Is () wide-sense stationary? a) Yes b) No 2) Find the cumulative d XtUtVtx UVEUEVEUEV Xt =++<¥ =="==" x="" 2="" 2="" 2="" 2="" 2="" 2="" istribution="" f(x)="P(Xx)" for="" the="" rv="" where="" its="" probability="" density="" is="" ()="" ,="" -.="" ,0="" ,0="" 2="" 2="" a)="" ()1="" ,="" b)="" ()="" c)()="" d)="" 1="" ,0="" 1,0="" 2="" 2="" x="" x="" x="" x="" x="" xxx="" x="" x="" fxex="" e="" e="" x="" x="" fxexfxfxf="" e="" ex="" x="" -="" -="" -="" -="" -="" -="" £=""><¥ ì="" ì=""><>< ï="" ï="" ïï=""><¥== íí="" ïï="" -³="" -³="" ï="" ï="" î="" î="" x="" ()1,="" 3)="" suppose="" the="" probability="" of="" having="" a="" d="" isease="" is="" .001,="" and="" a="" blood="" test="" is="" 100="" %="" effective="" in="" detecting="" the="" disease="" when="" the="" perso="" n="" has="" the="" disease.="" however,="" the="" test="" yie="" lds="" a="" "false="" po="" x="" x="" xex="" -=""><¥ sitive"="" for="" 1%="" of="" healthy="" persons="" teste="" d.="" what="" is="" the="" probability="" a="" person="" has="" the="" disease="" given="" that="" his="" test="" result="" is="" positive?="" is="" the="" answer="" a="" pproximately="" a)="" .44="" b)="" .01="" c)="" .09="" d)="" .90="" 4)="" a="" pair="" 6666="" 66="" k="1k=1" of="" fair="" dice="" is="" rolled="" six="" times.="" find="" the="" probability="" that="" a="" "six"="" will="" show="" at="" least="" once.="" 66="" 315553131="" a))1))1="" 363636363636="" 5)="" kkkk="" bcd="" kk="" --="" æöæö="" æöæöæöæöæöæö="" --="" ç÷ç÷ç÷ç÷ç÷ç÷="" ç÷ç÷="" èøèøèøèøèøèø="" èøèø="" åå="" let="" ()cos0where="" w="" is="" a="" constant="" and="" a="" is="" a="" uniform="" random="" variable="" over="" (0,1).="" the="" autocor="" relation="" (,)="" is="" cos()cos()cos()1="" a)1="" )))="" 332="" 6)let="" and="" be="" independent="" uniform="" rando="" m="" var="" x="" xtawtt="" rts="" tsst="" bcd="" xy="³" -="" iables="" over="" (0,="" 1).="" let="" z="." find="" the="" density="" ()in="" simplest="" form="" (not="" in="" terms="" of="" an="" integral).="" z="" xyfz="" +="" 7)="" a="" lot="" of="" 100="" items="" is="" examined="" y="" a="" te="" ster="" who,="" at="" random,="" takes="" 10="" pieces="" and="" checks="" their="" quality.="" if="" there="" is="" no="" defective="" among="" the="" 10="" items,="" the="" lot="" is="" accepted.="" what="" is="" the="" probability="" that="" a="" (="" )="" 1090="" 10="" lot="" which="" has="" 10="" defective="" pieces="" will="" b="" e="" accepted="" by="" the="" tester?="" 90="" 100="" 10="" 90898119="" a)="" 0.9="" b)="" c)="" d)="" 100100="" 10="" 10099911010="" 1090="" 8)="" the="" probability="" of="" a="" æö="" ç÷="" æö="" ××××="" æöæö="" èø="" ç÷ç÷="" ç÷="" ××××="" æöæö="" èøèø="" èø="" ç÷ç÷="" èøèø="" driver="" will="" have="" an="" accident="" in="" 1="" month="" equals="" .02.="" find="" the="" probability="" that="" in="" 100="" months="" he="" will="" have="" two="" acci="" dents.="" find="" the="" solution="" exactly="" and="" app="" roximately.="" (="" 9)="" given="" the="" joint="" density="" (,)="" c="" fxy="2" 22="" 2="" 2="" )01,01="" 0="" otherwise="" the="" conditional="" density="" of="" given="" any="" va="" lue="" of="" is="" for="" 01="" ()612()="" a)="" b)="" ()c)="" ())="" 1="" 1+y533="" +y="" 2="" 10)the="" moment="" generating="" function="" for="" an="" exp="" xyxy="" xyx="" cxyxy="" xxyd="" +££££="" ì="" í="" î="">< ++="" ++="" 11="" onential="" random="" variable="" with="" parameter="" is="" 1="" a)="" (1-j/),b),c)="" (1-/),),="" jtttdt="" tt="" l="" l="" wllwllll="" ll="" --="" ¹=""><> --