Every person in a natural populace is expected to conceive an offspring at a remarkable rate A, and to

kick the bucket at a dramatic rate u. Also, there is a dramatic pace of increment e due to

movement. Be that as it may, migration isn't permitted when the populace size is N or bigger.

(a) Set this up as a birth and demise model.

A, u = 2, decide the extent oftime that movement is limited.

Q50

A little barbershop: worked by a solitary stylist, has space for all things considered two clients. Potential

clients show up at a Poisson rate ot three every hour, and the progressive help times are

free dramatic irregular factors witn mean hour.

(a) What is the normal number of clients in the shop?

(b) What is the extent of potential clients that enter the shop?

(c) It the hairdresser could work twice as quick, what amount more business could he do?

Q51

In the wake of being fixed, a machine capacities for a dramatic time frame witn rate An and afterward falls flat. upon

disappointment, a maintenance interaction starts. The maintenance interaction continues consecutively through k unmistakable

stages. Initial a stage 1 fix should be performed, at that point a stage 2, etc. The occasions to

complete these stages are autonomous, with stage I taking an outstanding time with rate

(a) What extent of time is the machine going through a stage I fix?

(b) What extent of time is the machine working?

Q52

Allow the interaction to have 3 states, and the quantity of the state is equivalent to the number ot down

machines. As we can see this cycle is a birth and passing interaction. The boundaries of the

measure are

g - p, isl,2

We realize that for this cycle

time to go from _ jk (p

state k to state j z 'l Z g

Hence the normal worth ofthe time until the two machines are in the maintenance office beginning with

the two machines in the functioning condition is

time to go from 2O

state O to state 2 A

2

2

12 (A-A)

(b) We realize that for a birth and passing interaction

1

1

Along these lines: utilizing that E(T )

what's more, E(TO)

we have

time to go from

+ Var[Tll

Var

state 0 to state 2

1

2

1

A(R+Y) "+2

2

(c) The extent oftime there is a functioning machine over the long haul is equivalent to Po +8. We

realize that for the birth and passing cycle

Along these lines,

1

2

Hence,

2