In the following question, they have asked what are the issues surrounding the use of random number in simulation. You have given 5 points. Kindly elaborate the same.

 

Question:

 

Answer

Following are the issues surrounding the use of random numbers  in simulation:

1.Uniformity

2.Independence

3.Efficiency

4.Replicability

5.Long Cycle Length

Monte-carlo simulation technique requires the generation of a sequence of random numbers that is an integral part of the simulation model. The sequence of random numbers help in choosing random observations from the probability distribution.

Random numbers, used in simulation exercises are generated using digital computers.

 

*Multiplicative Congruential Random Number Generation Method:

Basic Relationship:

Xi+1 = a Xi (mod m), where a ³ 0  and  m ³ 0

Most natural choice for m is one that equals to the capacity of a computer word.

m = 2b (binary machine), where b is the number of bits in the computer word.

m = 10d (decimal machine), where d is the number of digits in the computer word.

The max period(P) is:

For m a power of 2, say m = 2b, and c ¹ 0, the longest possible period is P = m = 2b , which is achieved provided that c is relatively prime to m (that is, the greatest common factor of c and m is 1), and a = 1 + 4k, where k is an integer.

For m a power of 2, say m = 2b, and c = 0, the longest possible period is P = m / 4 = 2b-2 , which is achieved provided that the seed X0 is odd and the multiplier, a, is given by a = 3 + 8k or a = 5 + 8k, for some k = 0, 1,…

For m a prime number and c = 0, the longest possible period is P = m – 1, which is achieved provided that the multiplier, a, has the property that the smallest integer k such that ak – 1 is divisible by m is k = m – 1,

 

In the given demonstration , Xi+1 = a Xi (mod m)

Here, a=6, m=17, x0=1, since m-1=16 is the 2 digit random number, therefore it will generate 2-digit random numbers.

So, X1 = a X0 (mod m)=6*1(mod 17)=6/17=06

X2 = a X1 (mod m)=6*6(mod 17)=36/17=02

X3 = a X0 (mod m)=6*2(mod 17)=12/17=12

 

 

The student got the following answer from one of his friend.  Please provide your suggestions for the answer given.

 

Question : What are the issues surrounding the use of random number in simulation.

Answer : Random numbers are integral part of simulation as it allows verification of model based on unbiased number generation. However there are multiple random number generation techniques varying from simple to complex calculation. Every model can only respond to particular set of random numbers only. Therefore it becomes quintessential to pin point random number generation technique to be used for any specific model.

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