Hi, I need this work done, I need to know exactly how much time it will take.
(1) (a) Write a computer program to generate random numbers between [0,1]. Such a random number generator simulates the values generated by a uniform random variable U[0, 1].
(b) Write another progam (using the program in (a)) to estimate P(U > x). Plot P(U > x)
for values of x 2 (0.5, 1).
(2) (a) Write a computer program to simulate the values generated by Exponential (X) and Poisson random (Y ) variables using the program you developed in (1).
(b) Provide plots for P(X > x) and P(Y > x), for E(Y ) = E(X) = 2. It may be necessary
to show your result on a plot where the vertical axis is logarithmic.
(3) (a) Write a computer program that simulates an M/M/1 queue.
(b) Based on this program plot Pn against n when λ = 5 and µ = 6.
(c) Again, from your program, find the expected number and expected delay in your M/M/1 queueing system when ρ= 5/6.
(4) (a) Write a computer program that simulates an M/Ek/1 queue. Here, Ek is an Erlang
random variable with k phases.
(b) Based on this program, plot Pn against n when k = 4, λ = 5 and µ = 6. Also, find
the expected number in the system. How do these results compare with your M/M/1
results in (3)?
(c) Plot the expected number in the system for different values of the utilization when
k = 40. Also plot the expected number in the system in an M/D/1 queue from the
analysis in class and compare the results with your simulation. What does this tell you
2) Installation package that will install the software (in ready-to-run condition) on the platform(s) specified in this bid request.
3) Exclusive and complete copyrights to all work purchased. (No GPL, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site).