Esercitazione svolta per preparazione esame Financial mathematics

Guzzinatieusabetta 7125306ex 1

Balla30b b black 11b129bolls=W bollsWhite >w 30-PW= =replacementwithoutbolls2drowwe wi ball dramnI for black10we anyi :

a) 18ball extractionblack atBr theevent I .drow a= 2"the extractionblackI bellBz event atdrow .a=P(B2) Po 14bell afof blackProbablity thedrawing= aextraction . 15isn't replacement B2There theextractionthe eventafter is> so,by Bseventtheconditionated .P(B2) #1 HiP(B11Bz) of bell teatblackprobability drawing e= = = a22d extraction .knowing the formula :P(A(B) P)AnB= P(B) (B21B2)PbellsblackProbability 2 :drowwe- =P(B2)P(B21B2) =P(B2(Be)= .

b) 18IeventWe white ofball extractiondrow thea= 2"d extractionIevent bellwhite theWe atdrow a=P(W2) =P(WzlWe) == P(WelWabellswhite2-Probability :drowhe bbP(we) b2P(W21Wz) +59b(W2(W2) === .. - 870

c) P(B2) =P(Wz/B2) 30- e= = P(B2) eP(W2nB2) (W2(B2) . byD. == =in :X-event drow 2 bollsweE[X] 15>, 1Wz)](BenB2)] (B11W2)] P(W2E[X] [P [P220 10 ++ 0= ...

d ↳ get for Iget=> wewe black belltwofor blackbells s/22/3 e/ /22b2 60b-2b 2b+- 157,87& Db 23 b23 22 5:>- Incont to have- E[x]> We 15, order, , >,>-(87 integeran3 bellsof blackthe umber have toin baxthebe leastof 23.

Ex2

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