Make Random Numbers Tend / Average to a Specific Value

Question

How can I for example generate a list of random numbers between 0 and 1, but have them avarage at 0.8?

I have written this little script in C++ that\'ll tell you wh

Answer 1

Here's an example that generates a standard normal distribution, i.e. mu = 0, sigma = 1.

I used the Box-Muller transform.

All plots have x axis = value and y axis = frequency.

#include 
#include 
#include 
#include 
int main(int argCount, char** argVector) {
    const double pi = 3.14159265359;
    const double nums = 1000000;
    double u, v, x;

    srand(rand() + (int) time(NULL));

    for(unsigned int i = 0; i < nums; i++){
        u = rand() / (((double)RAND_MAX) + 1.0);
        v = rand() / (((double)RAND_MAX) + 1.0);
        x = sqrt(-2*log(u)) * cos(2*pi*v);

        if (std::isfinite(x)){
            std::cout << x <<" ";
        }
    }

    return 0;
}

>>> np.std(nums)
1.0004139708929858
>>> np.average(nums)
7.1785002756408726e-05

You can shift/scale x as necessary to obtain a mu and sigma of your choosing.

Here's an example that gives a uniform distribution with a given mu:

#include 
#include 
#include 
#include 
int main(int argCount, char** argVector) {
    const double pi = 3.14159265359;
    const double nums = 1000000;
    double x,mu;

    srand(rand() + (int) time(NULL));
    mu = 3.0;

    for(unsigned int i = 0; i < nums; i++){
        x = rand() / (((double)RAND_MAX) + 1.0);
        x *= 2*mu;

        if (std::isfinite(x)){
            std::cout << x <<" ";
        }
    }

    return 0;
}

>>> np.average(nums)
3.0003091558133184

You can use the documented rand() % range + min to truncate.