Question

1. Consider a linear congruential random number generator with parameters a = 3,

m = 16, and c=0.

• Select the seed X0 = 3, and generate 3 random variables using this generator.
• What is the period of this generator?

Answer 1

SOLUTION:

From given data,

Consider a linear congruential random number generator with parameters a = 3,m = 16, and c=0.

a = 3,

m = 16,

c=0.

The recurrence relation to define generator is

X_n+1 = (a X_n+c) mod m

here X is sequence of random numbers

and X₀ is referred to seed which is also called start value.

Select the seed X₀ = 3, and generate 3 random variables using this generator.

No we have X₀ = 3, we need to generate three random numbers with it

as we are starting with n = 0 (X₀)

X₁ = (a*X₀ + c ) mod m

X₁ = (3*3 + 0) mod 16

X₁ = 9 mod 16

X₁ = 9

Now let us try X₂

X₂ = (a * X₁ + 0) mod 16

X₂ = (3*9 + 0) mod 16

X₂ = 27 mod 16

X₂ = 11

Now X₃

X₃ = (a * X₂ + 0) mod 16

X₃ = (3* 11 + 0) mod 16

X₃ = 33 mod 16

X₃ = 1

What is the period of this generator

Period of Generator :

When c = 0 then generator is call multiplicative congruential generator and period of MCG is at most m