Radioactive Decay, Gaussian or Uniform? I'm trying to understand the nature of true randomness. I'm building an RNG using a radioactive source. Basically, I'm measuring the time between consecutive decays which in theory should be unpredictable. The distribution of these time measurements shows a Gaussian-like distribution as I predicted. Now my understanding of true randomness requires a uniform distribution of variables, which is all variables are equally likely. How can I transform a Gaussian Distribution to uniform distribution and is it really necessary to have uniformly distributed random bits to have a good generator?
You can just follow the instructions on HotBits, which is exactly what you're trying to build. It's been running for years and is the only radioactive TRNG on the internet. It goes into great depth regarding underlying nuclear physics, sample distributions and extractor mechanism.
Although not really within the realms of strict cryptography, there is also a good counting analysis here from Caltech. In a nutshell, at low count rates the click rate follows a Poisson distribution. But as the mean click rate $(\mu$) increases, it morphs into a nice symmetrical Gaussian shape which is typical behaviour of Poisson if $\mu &gt; \approx 20$.
If you can get a good tube and a decent/safe source, it'll be pretty simple if you follow the instructions.  Don't worry about the tick distribution. Simply detect the ticks and follow the de-biasing procedure in the sections featuring this:-

It's a reversing von Neumann extractor. It's written up so I won't repeat the details. If tube dead times and saturation levels are met (so that there is no autocorrelation), you'll get uniformly distributed random bits popping out of the de-biasing algorithm. So that we can see HotBits' quality, I downloaded their 91 Mbit data set and ran ent over it:-
Entropy = 1.000000 bits per bit.

Optimum compression would reduce the size
of this 91750400 bit file by 0 percent.

Chi square distribution for 91750400 samples is 0.05, and randomly
would exceed this value 81.93 percent of the times.

Arithmetic mean value of data bits is 0.5000 (0.5 = random).
Monte Carlo value for Pi is 3.141486168 (error 0.00 percent).
Serial correlation coefficient is -0.000773 (totally uncorrelated = 0.0).

They have other more stringent testing on their site, but it's a clean pass at this level. Chi square also answers your &quot;is it really necessary to have uniformly distributed random bits to have good generator?&quot; mini question. Yes, they do have to be uniformly random for cryptographic use.
So do what HotBits does.

Please note this though:-

the increased sensitivity of the RM-80 and its immunity from saturation increased the rate of HotBits generation from about 30 bytes per second to more than 100.

It's not fast. And there's all that high voltage stuff.