Simulation and modeling - Old Questions

Question Answer Details

11. Use the multiplicative congruential method to generate a sequence of four three-digit random numbers. Let X₀=118, α=4 and m=1000.

5 marks

Asked in 2069

Answer

AI Generated Answer

Official Answer

Given,

X₀= 118,

α = 4,

m=1000

We have,

For multiplicative congruential method:

X_i+1 = (α X_i) mod m

& R_i=X_i/m,

The sequence of random numbers are calculated as follows:

X₀= 118

R₀ = 118/1000 = 0.118

X₁ = (α X₀) mod m = (4*118) mod 1000 = 472 mod 1000 = 472

R₁ = 472/1000 = 0.472

X₂ = (α X₁) mod m = (4*472) mod 1000 = 1888 mod 1000 = 888

R₂ = 888/1000 = 0.888

X₃ = (α X₂) mod m = (4*888) mod 1000 = 3552 mod 1000 = 552

R₃ = 552/1000 = 0.552

X₄= (α X₃ ) mod m = (4*552) mod 1000 = 2208 mod 1000 = 208

R₄= 208/1000 = 0.208

Therefore,

The sequence of random integers are 118, 472, 888, 552, 208.

The sequence of random numbers are 0.188, 0.472, 0.888, 0.552, 0.208.