I only have a uniform distribution function between [0,1]. And from this distribution, I should generate a sequence of Rayleigh distributed random variable using some software.

Anyhow, I was able to finish the problem using the formula from the Wikipedia article:

However, there is only one thing I could not understand. I tried many times to find the previous formula using the Inverse transform sampling method, but no use.

Can someone show me the steps of how X was found?

I only have a uniform distribution function between [0,1]. And from this distribution, I should generate a sequence of Rayleigh distributed random variable using some software.

Anyhow, I was able to finish the problem using the formula from the Wikipedia article:

$$(1)\;\;\;\;X=\sigma\sqrt{-2\ln(U)}$$

However, there is only one thing I could not understand. I tried many times to derive formula $(1)$ using the Inverse transform sampling method, but I could not.

Can someone show me the steps of how $(1)$ is found?