IIExRcrsEs8lWcconsidcrthcdiscrctcdistributiorofEramplc25.3.ThcFMGFofX isGAt)=MArtt)= I t 3].(e) Findlhc probabilitylhatthc scorcii an odd inlctcr.3.A bag conlaintthrcccoins,oneofwhichha.sahcadonbolhsidcJ whilcthcothcrlwocointatcnormal.A coinii choscnatrandomfrom thcbagsnd torscd lhra.limcs'Th'nl,mbcrolhcadsis arandomvariablc,say X.(a) Findlhc discrct. pdfofx.(Hir!: Usc lhc LawofTolalP.obability with8r =anormalcoinand Br - two-hcadcdcoin.)(b) stctch lhc discrcl. pdf andthc CDFofX.t.A bor containr6vccolotcdballs,two blackand thrccwhilc.Balls arc drawnsucctstivclys/ithoutt.plaemcnllf X is thc numbcroldraws!ntil lhc laltblackballisobtaincd,findthc di56ctc pdtl(r}, '.r' A discrclcrandomvariablchar pdfl(x).lal lff(xl -Hll2Y forx - 1,2,3,andzctoothcrwisc,find r((b) Is afunctionoflh. foft I$l-kUIPY-ll2l fo.x-0,l,2aPdfforany,t?6.Dcnolcby [x] thc Srcalcst intcSc.no!cxcscdingx.For thc Pdfin Eramplc211,showlhatthcCDFcanbctcPrcacntedasF(x) - ([x]/12)tfor0 2].(d) Find E(xIy 8.A nonnc8ativcinlcgc.-valucdr.ndomvariabl.X ha5aCDF otthcformF(x)-I - (lPF'I for x-0, l,1,,.andzcroifx