Question

Professor Sun’s home uses two light bulbs. On average, a light bulb lasts for 22 days (exponentially distributed). When a light bulb burns out, it takes an average of 2 days (exponentially distributed) before he replaces the bulb. (a) Formulate a three-state birth-death model of this situation. (b) Determine the fraction of the time that both light bulbs are working. (c) Determine the fraction of the time that no light bulbs are working.

Answer 1

Solution Fhom the Juen data, a) Lt the State mumber of thi working bulbs Possible Status aru o,, and Budh bulb upairid, while Death bulbs batm out Thum the bilh death Paha mdurs ahu as tlloud + 2 1 + 22 221 Stady state phobabilday may b found fhom . 22 + T 17

+ (07) 22 Thus no ( 22+ 121)-1 11 T 121 144 144 b 121 44 1-7 144
Thank you.