Randon Number Generation – QAWS Operations Research

There are many different ways to generate random numbers on a computer, most random number generators use the linear congruential relationship. This congruential generator produces a sequence of integers $x_{1}, x_{2}, x_{3}, . . .$ between $0$ and $m - 1$ : $R_{i} = \frac{x_{i}}{m} (i = 1, 2, 3, . . .)$

The initial value $\dpi{100} \fn_jvn x_0$ is the seed, $\dpi{100} \fn_jvn a$ is the constant multiplier, $\dpi{100} \fn_jvn c$ is the increment, and $\dpi{100} \fn_jvn m$ is the modulus. The value value of $\dpi{100} \fn_jvn x_{i+1}$ equals the reminder from the divison of $\dpi{100} \fn_jvn ax_i+c$ by $\dpi{100} \fn_jvn m$ . The random number between 0 and 1 is then generated using the equation:

$\dpi{100} \fn_jvn R_i = \frac{x_i}{m}\; \; \; \; (i = 1,2,3,...)$

We use the class ‘Random’ in .NET Core, which used the system clock as seed:

– Random floating-point number that is greater than or equal to 0.0, and less than 1.0:

static Random randomX = new Random();
decimal rnX = Convert.ToDecimal(randomX.NextDouble());

– Random number number that is greater than or equal to x, and less than y:

static Random randomX = new Random();
decimal rnX = Convert.ToDecimal(randomX.Next(x, y));

The probability factor

Suppose it is required to generate random numbers using a probability component