Question

1. Suppose that when a type of transistor is subjected to an accelerated life test, the lifetime Y (in weeks) has a gamma distribution with mean 12 weeks and standard deviation 6 weeks (a) What are the values of a and B? (b) What is the probability that a transistor will last between 9 and 15 weeks? (c) What is the probability that a transistor will last at most 12 weeks? (d) What is the median of the lifetime distribution? (e) What is the 90th percentile of the lifetime distribution? (f) Suppose the test will be terminated after t weeks. What value of t is such that only 1% of all transistors would still be operating at termination?

show work please

Answer 1

Saln amma dismbution ilt mean 12 uweeas &tandasd deiahon 6 seelas andl palameters 7amma dshb- The pel Let and p be the givan by uhen Such that Ja 12 12p we Knew E(X) mean and 36 D.)= (X)A 32 gel 12- 36 B = 363 7 2 e Tpe dtere (b) P(A hansistor weill last between andis 3 -Q 2- e 3, dx weeks) -PC9XSIS) 39 *p (0)X ! I5 da xe 3IX0 e 2/3 +3 Now T 20 3xe 3 11 + +

3dn 3x e 37 x.e +37X2 - 3 2e 3 e -27 x e dx 3 x/3 27x e l3 162X3e 3 e 162xe 2 PC a hramsestr acill Last behween 9 andweeks cen 4863 3x-27x-16 2x e xt27xt162xty06) e 6X0) S3 (327x0t 162 )e 406 +(3x()27x3tl62x9+40e -C- 19116xe6310xe 406 486 -19116xe+ 314.34690 120. 00x90+314 4690]X i05.7581 T06 406 03022 AS 11

CC P(a hansist citl lost ahmest 12 weeks) Spladdn 20. x+37xt162xt 406)e 6X81 -20/3 (62x0t406)e 27 (20) 406 0t 406-100520)-e 406 1406-49.0274070 406 436 92o 93 406 (d) whaot Life tome is the medean Know that dis tmhon such hal Ne Lo'S O -3x+27t1622t406)e 406 C486-(327262 e= oang ris uumei medeam r we Can obtaawed we prow Thal Le olis fi bulipw ta elosed imple form 6 meelaan JAmma