The two questions are equally weighted. 1. The probability of a program terminating successfully in the first hour of execution is given by the area under the curve: y = x3 - x2 + e-x between x = 0...

The two questions are equally weighted.
1. The probability of a program terminating successfully in the first hour of execution is given by the area under the curve: y = x3 - x2 + e-x between x = 0 and x = 2. Carry out a Monte-Carlo simulation to estimate the area under the curve between x = 0 and x = 2. You should include in your answer:(a)Your code developed to carry out this task;(b)The value that you have estimated for the area, and a discussion of how the accuracy of the estimation varies with the number of iterations and how many iterations are required to ensure the desired accuracy.
2. Consider the following queuing system, where workload arrives at a web server at a Poisson rate of one job every 25 milliseconds. Service at the web server is exponential, with mean 5 milliseconds. On completion of this task the jobs then queue for access to a data centre. Each job spends a period of time at the data centre which is uniformly distributed, between 8 and 12 milliseconds. After data centre service is completed the job either terminates, with probability 0.9, or it returns to the web server queue, with probability 0.1, and proceeds as before.(a)Draw a queuing diagram to represent the system.(b)Provide pseudocode to show how a simulation program for this system would work.(c)Write a program using SIMUL8 to simulate this system. Use one millisecond as the unit of clock time.(d)Run your simulation program to generate results over a period of 1 minute of clock time.(e)Analyse the performance statistics that are produced as output from your program. Is this an efficient system? Use your SIMUL8 program to investigate how you might improve overall performance.In your submission you should include:•A summary of your findings;•Your program.