Satellites are dispatched by a Poisson interaction with rate A. Each satellite will,

freely, circle the earth for an irregular time frame having dispersion F. Allow {X(t)} to signify the

number of satellites circling at time t

(a) Determine = k)

Clue: Relate this to the line.

(b) It in any event one satellite is circling, at that point messages can be sent and we say that the

framework is utilitarian. Ifthe first satellite is circled at time t = O, decide the normal time that

the framework stays utilitarian.

Clue: Make utilization of section (a) when k - O.

Q68

Every one of n skiers ceaselessly, and freely, scales and afterward skis down a specific slant.

The time it takes skier I to scale has dispersion Fi, and it is free of her chance to ski

down, which has conveyance HI, j = 1, .

, n. Let signify the absolute number of times individuals from this

bunch nave skied down the slant by time t. Additionally, let U(t) signify the quantity of skiers scaling

the slope at time t.

(a) What is limt*N

Find

(c) It all F/are remarkable with rate An and all Gi are outstanding with rate g, what is

Q69

There are three machines, all ofwhich are required pinnacle a framework to work. Machine I works for

a dramatic time with rate before it comes up short, j = 1, 2, 3. At the point when a machine fizzles, the framework is closed

down and fix starts on the bombed machine. An opportunity to fix machine 1 is outstanding with rate

5; an opportunity to fix machine 2 is uniform on (0: 4); and an opportunity to fix machine 3 is a gamma

arbitrary variable with boundaries n - 3 and A = 2. When a followed machine is fixed, it is as great

as new and all machines are restarted.

(a) What extent of time is the framework working?

(b) What extent of time is machine 1 being fixed?

(c) What extent of time is machine 2 in a condition of suspended activity (that is, not one or the other

working nor being fixed)?

Q70

A transporter consistently drives full circle trips from one A to another and afterward back to A. Each time ne drives

trom A to B, he drives at a fixed speed that (in miles each hour) is consistently appropriated between 40

also, 60; each time he drives trom a to A, he drives at a fixed speed that is similarly prone to be

either 40 or 60.

(a) In the since quite a while ago run, what extent of his driving time is spent going to B?

(b) In the since a long time ago run, for what extent of his driving time is he driving at a speed of 40 miles for each

hour?