A spotlight needs two batteries to be operational. Consider such an electric lamp alongside a bunch of n

practical batteriesbattery 1, battery 2,

. battery n. At first, battery 1 and 2 are introduced.

At whatever point a battery tails, it is quickly supplanted by the least numbered practical battery

that has not yet been placed being used. Assume that the lifetimes of the various batteries are

autonomous outstanding arbitrary factors each having rate u. At an arbitrary time, call it T, a

battery will tail and our reserve will be vacant. At that point precisely one ofthe batteries

which we call battery Xvvill not yet nave followed.

(a) What is P{X-n}?

(b) What is

(c) What is

(d) Find E[T].

(e) What is the dissemination of T?

Q18

Clients can be served by any of three workers: where the help seasons of worker I are

dramatically circulated with rate gj, i= 1, 2, 3. At whatever point a worker turns out to be free, the client

who has been holding up the longest starts administration with that worker.

(a) It you show up to track down every one of the three workers occupied and nobody pausing, figure out the normal time until you

withdraw the framework.

(b) It you show up to track down every one of the three workers occupied and one individual pausing, figure out the normal time until

you withdraw the framework.

Q19

Each entering client should be served first by worker 1, at that point by worker 2, lastly by worker

3. The sum oftime it takes to be served by worker j is an outstanding irregular variable witn

rate gj, I = 1, 2, 3. Assume you enter the framework when it contains a solitary client who is being

served by worker 3.

(a) Find the likelihood that worker 3 will in any case be occupied when you move over to worker 2.

(b) Find the likelihood that worker 3 will in any case be occupied when you move over to worker 3.

(c) Find the normal sum oftime that you spend in the framework. (At whatever point you experience a

occupied worker, you should trust that the help in progress will end before you can enter administration.)

(d) Suppose that you enter the framework when it contains a solitary client who is being served by

worker 2. Track down the normal sum ot time that you spend in the framework.

Q20

Leave X and Y alone free remarkable irregular factors with separate rates An and g, where A

> g. Letc>O.

(a) Show that the restrictive thickness capacity of X, given that X + Y = c, is

fXlX+Y (xlc) =

(b) use section (a) to discover E[XIX+ Y

(c) Find EIYIX+ c].