The question posed came about during a 2nd Year Comp Science lecture while discussing the impossibility of generating numbers in a deterministic computational device.
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Part of a good random number generator is equal probabilities of all numbers as n -> infinity.
So if you are planning to generate random bytes, then with sufficient data from a good rng, each byte should have an equal probability of being returned. Further, there should be no pattern or predictibiltiy (spikes in probability during certain time periods) of certain numbers being returned.
I am not too sure with using ping what you would be measuring to get the random variable, is it response time? If so, you can be pretty sure that some response times, or ranges of response times, will be more frequent than others and hence would make a potentially insecure random number generator.