Simulation and Modelling - Old Questions

8. Use mixed congruential method to generate a sequence of random numbers with X0 = 27, a = 17, m = 100 and c = 43. 

Given,

    X₀ = 27, 

    α = 17,

    c= 43 &

    m=100

We have,

        X_i+1 = (α X_i + c) mod m

        Mixed Congruential Method: c ≠ 0

        & R_i =X_i/m,

The sequence of random numbers are calculated as follows:

X₀ = 27

R₀ = 27/100 = 0.27

X₁ = (α X₀ + c) mod m = (17*27+43) mod 100 = 502 mod 100 = 2

R₁ = 2/100 = 0.02

X₂ = (α X₁ + c) mod m = (17*2+43) mod 100 = 77 mod 100 = 77

R₂ = 77/100 = 0.77

X₃ = (α X₂ + c) mod m = (17*77+43) mod 100 = 1352 mod 100 = 52

R₃ = 52/100 = 0.52

X₄ = (α X₃ + c) mod m = (17*52+43) mod 100 = 927 mod 100 = 27

R₄ = 27/100 = 0.27

Therefore,

The sequence of random integers are 27, 02, 77, 52, 27 & so on.

The sequence of random numbers are 0.27, 0.02, 0.77, 0.52, 0.27 & so on.