如何在给定标准差（sigma）的PHP中创建正态分布的随机数？

Question

I need normally distributed random numbers. Therefore I implemented the Polar Method like its mentioned here:

Polar Method

That's working good. But my problem is it only gives me standard normally distributed random numbers. But I also need some with another standard deviation(sigma).

So I would need this generator to generate normally distributed random numbers with a given standard deviation(sigma).

At the moment I am only able to create something like the blue one (standard): Graphics

Is this possible?

Answer 1

Standard normally distributed random numbers have a standard deviation equal to 1. If you just multiply those random numbers by X, where X is a positive number, then you create normally distributed numbers which have a standard deviation equal to X :-).