Use the mixed congruential method to generate a sequence of five 2-digit random integer numbers such that xn+1 = (41xn + 33) (modulo 100) and x0 = 48
-
Carrying out the sequence, we start with:
x[0] = 48
Then,
x[1] = (41x[0] + 33) mod 100
= (41*48 + 33) mod 100
= (1968 + 33) mod 100
= 2001 mod 100
= 1
But that's not a 2-digit integer. So, we continue with x[1] = 1 as the "seed" for the next value:
x[2] = (41x[1] + 33) mod 100
= (41*1 + 33) mod 100
= 74 mod 100
= 74
x[3] = (41x[2] + 33) mod 100
= (41*74 + 33) mod 100
= 3067 mod 100
= 67
... and, continuing in this way,
x[4] = 80
x[5] = 13
x[6] = 66
So, our sequence of five 2-digit pseudorandom integers begins at x[2], continuing through x[6]:
74, 67, 80, 13, 66
x[0] = 48
Then,
x[1] = (41x[0] + 33) mod 100
= (41*48 + 33) mod 100
= (1968 + 33) mod 100
= 2001 mod 100
= 1
But that's not a 2-digit integer. So, we continue with x[1] = 1 as the "seed" for the next value:
x[2] = (41x[1] + 33) mod 100
= (41*1 + 33) mod 100
= 74 mod 100
= 74
x[3] = (41x[2] + 33) mod 100
= (41*74 + 33) mod 100
= 3067 mod 100
= 67
... and, continuing in this way,
x[4] = 80
x[5] = 13
x[6] = 66
So, our sequence of five 2-digit pseudorandom integers begins at x[2], continuing through x[6]:
74, 67, 80, 13, 66