Gaussian random values. Implement the no-argument gaussian() function in StdRandom (PROGRA...

Gaussian random values. Implement the no-argument gaussian() function in StdRandom (PROGRAM 2.2.1) using the Box–Muller formula (see EXERCISE 1.2.27). Next, consider an alternative approach, known as Marsaglia’s method, which is based on generating a random point in the unit circle and using a form of the Box–Muller formula (see the discussion of do-whi 1 e at the end of SECTION 1.3).

public static double gaussian(){   double r, x, y;   do   {       x = uniform(−1.0, 1.0);       y = uniform((−1.0, 1.0);       r = x*x + y*y;   } while (r >= 1 || r == 0);   return x * Math.sqrt(−2 * Math.log(r) / r);}

For each approach, generate 10 million random values from the Gaussian distribution, and measure which is faster.

EXERCISE 1.2.27

Gaussian random numbers. Write a program RandomGaussian that prints a random number r drawn from the Gaussian distribution. One way to do so is to use the Box–Muller formula

r = sin(2 πv) (−2 ln u)1/2

where u and v are real numbers between 0 and 1 generated by the Math.random () method.

Program 2.2.1 Random number library