Drd0 2008 q-11 ch-3 i/o interface

Question

 In an n- CPU shared bus system, if z is the probability that any CPU requests the bus in a given cycle, the probability that only one CPU uses the bus is given by-

A. Nz(1-z)^n-1 

B. Z(1-z)^n-1

C. N(1-z)ⁿ

D. (N-1)z(1-z)ⁿ

Answer 1

OPTION A.

There are N - CPUs , and exactly one of them uses the bus.

Using binomial distribution, ⁿC_x  * p^x * (1- p)^n-x  

                  { Here x is number of success , p is probability of success in one trial,

                    n is total number of trials }   

---

probability that only one CPU uses the bus  =  ^NC₁ * z¹ * (1-z)^N-1   = A(Ans)  

                      {Here z is probability  of CPU using bus & we want exactly one Cpu to use the bus

                        at a time so,   ^NC₁ }..