Question

Two towns, Besiktas and Sariyer are going to raise a fund together to build a new public library. Suppose Besiktas will raise B million Turkish Liras and Sariyer will raise S million Turkish Liras. B has exponential distribution with rate 1.1 and S has exponential distribution with rate 1.7. Suppose B and S are independent. The new library will be built if they can raise 4 million Turkish Liras or more. What’s the probability that Besiktas will raise less than 2 million Turkish Liras given that the library can be built?  (P(B<2 | B+S≥4)=?)

Answer 1

Spl Contido the folloesing regions ६ (4,0) BAS: 4 S=4-B mathematically, we Can woile A as A: S (BS) S?0.7 if Boy and {cas S 24-D r(61524) - s folw) fs(y) dudy (n.)EA e", uzo where { p.d.f of B and 0, otherwise fs (y) = S(2.4) e (2:44 yo ştanish otherwise Similarly, Consider the following region.

2 (4,0) This region is {Be2, Bt Say? =c, say A (4,0) B = 2 S-4-B : mathematically, we can write ca (B.S) Io<BC 2 S24-0 .s) | P(StB 24, B (2) = fg (2) Is (y) dudy (hy) EC Now, P(S+B34) &B (1) fs (y) dudy (M,y) EA S { 5 (24) - (2.44 4-k dy } edut (2.479 dy} & "an 2 e 4 - (2.404 Now, $ (24) elan dy = fou fs (y) dy = 1 {p() isa p.de

3 and ۹-۱ و دوات (۸۱) *[ و(۱ ) و - [(24)لاہا) ع -5) - e -ال e (2) ( - ) e با :: ۲( 516 2 ) (۷-ها) (2) - ما : ) (۷۰*۵۰۰ ۱۰۵۷ :: (0 -- ( ا 서 ۹۰b - e (۱۹۹۹) -- ا -2 < 6- ۹:( (. e - ۹۰ e صد +Q e ۹۰ے ا - و + and, (اجى +6 62 )F 2 S fe (W) Is(y) dady: [ (ا .2) - و (2) : اده en du ع ع (9) - (2.1)(1-1)

14 S e el (2.4-10 du 2 è 9.6 (1.4) up interna (pousa]?- és (24 -1) 1.44 P(BC2 | Bts 24) P(B<2, Bts 24) PCB+524) - ė 96 (229,-) - 4 e -9-6 . eh + ୧ ñ 0.02383347 Please give me an upvole.