Question

During an eight-hour shift, the proportion of time Y that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with a 1 and B 2. That is, 2(1 - y), 0s ys 1, f(y) lo, elsewhere. The cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by C your answers to two decimal places.) 50Y 2y. Find the mean and variance of C. (Round 10 E(C) $ V(C)

Answer 1

Sol yn Beta (a,b) where al and B-2. we shall compute Ely) E(**)> [idas) **y 20-11-2) at de *360,0) S'kanke$(1-x) * 'de isla, b)x8(+2, BD (3) Tur) = B(k+1,2) B(1,2) =r(k+1) (2) (k+3) - Matej x 2 (2+)Ck+2) Hence, given | = lo +5% }+ 2y^ - E (9) - 9 3 E (9 ): 2 (9+1)(2+2) 6 (1+1)(1+2) E (4")= 1 / Now E(): 10 + 50 E(9) + E (92): 10+ $o + 2*4 = 10+17 ECC) = 27] dollars. Also CP. (1o+soy +9y2,2 = 100 + 250042 +444 +1000y + gooy} + 4072 E((?) = 100+ 4 E(49) + 200 ECY) +000 £19) + 2540 Ey? : 100+ us + 20 + 1000 + 2540 = 1876.93) VCC) = ECCO) - [Ecco)2 = 876.93 - 69738 = 147.93) so