Ajob shop consists of three machines and two repairmen. the amount of time a machine works before breaking down is exponentially distributed with mean 10. if the amount of time it takes a single repairman to fix a machine is exponentially distributed with mean 8, then(a) what is the average number of machines not in use? (b) what proportion of time are both repairmen busy?

Step-by-step explanation:

Let X(t) denote the number of machines breakdown at time t.

The givenn problem follows birth-death process with finite space

S={0, 1, 2, 3} with

The birth-death process having balance equations

since, state  rate at which leave = rate at which enter

            0      

             1    

             2  

Since

a)

Average number not in use equals the mean of the stationary distribution

b)

Proportion of time both repairmen are busy

i'm not sure i quite understand, could you provide more information?

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or