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Tribhuvan university CSIT 2065 Syllabus Simulation and modeling Old Questions 2071

Simulation and modeling - Old Questions

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Syllabus Notes Old Questions Unit Wise Questions Question Bank

10.  Use the multiplicative congruential method to generate five three digit random integers. X0=118, α=45 and m=1000.

5 marks
Asked in 2071

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Official Answer

Given,

    X0 = 118, 

    α = 45,

    m=1000

We have,

For multiplicative congruential method:

        Xi+1 = (α Xi ) mod m

The sequence of random integers are calculated as follows:

X0 = 118

X1 = (α X0) mod m = (45*118) mod 1000 = 5310 mod 1000 = 310

X2 = (α X1) mod m = (45*310) mod 1000 = 13950 mod 1000 = 950

X3 = (α X2) mod m = (45*950) mod 1000 = 42750 mod 1000 = 750

X4= (α X3 ) mod m = (45*750) mod 1000 = 33750  mod 1000 = 750

X5= (α X4 ) mod m = (45*750) mod 1000 = 33750 mod 1000 = 750

Therefore,
The sequence of random integers are 118, 310, 950, 750, 750, 750.