794 views
1 votes
1 votes

Suppose that the running time for each process in milliseconds is an exponential random variable with parameter λ=1/20. If process P1 arrives immediately ahead of the process P2 in the running state, then the probability that process P2 will have to wait more than 20 milliseconds is _____________ .

A
0.274
B
0.324
C
0.428
D
0.368

How to approach this. even not able to understand the question.

1 Answer

0 votes
0 votes

p(X>20 millsec) = 1 – p(X<= 20 millsec) ----- (1)

PDF = lamba. e^(-lamba.x)

CDF = p(X<= 20 millsec) = integral x from -infinity to 20 (PDF).dx

   = 1 – e^(-lamba*20)   ( given lamba = 1/20)
   = 1 – e^-1   -------(2)

sub 2 in 1.

p(X>20 millsec) = 1 – (1 – e^-1)  = e^-1 = 1/e = 0.36787944117 ~ 0.368  : option(D)

Related questions

0 votes
0 votes
0 answers
3
Na462 asked Feb 20, 2019
482 views
0 votes
0 votes
0 answers
4