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Tribhuvan university CSIT 2065 Syllabus Simulation and modeling Old Questions 2068

Simulation and modeling - Old Questions

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Syllabus Notes Old Questions Unit Wise Questions Question Bank

11.  Use the mixed congruential method to generate a sequence of three two-digit random numbers with X0=37, α=7, c=29 and m=100.

5 marks
Asked in 2068

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Official Answer

Given,

    X0 = 37, 

    α = 7,

    c= 29 &

    m=100

We have,

        Xi+1 = (α Xi + c) mod m

        Mixed Congruential Method: c ≠ 0

        & Ri =Xi/m,

The sequence of random numbers are calculated as follows:

X0 = 37

R0 = 37/100 = 0.37

X1 = (α X0 + c) mod m = (7*37+29) mod 100 = 288 mod 100 = 88

R1 = 88/100 = 0.88

X2 = (α X1 + c) mod m = (7*88+29) mod 100 = 645 mod 100 = 45

R2 = 45/100 = 0.45

X3 = (α X2 + c) mod m = (7*45+29) mod 100 = 344 mod 100 = 44

R3 = 44/100 = 0.44

Therefore,

The sequence of random integers are 37, 88, 45, 44

The sequence of random numbers are 0.37, 0.88. 0.45, 0.44.