Understanding “randomness”

Question

I can\'t get my head around this, which is more random?

rand()

OR:

rand() * rand()

I´m f

Answer 1

Most rand() implementations have some period. I.e. after some enormous number of calls the sequence repeats. The sequence of outputs of rand() * rand() repeats in half the time, so it is "less random" in that sense.

Also, without careful construction, performing arithmetic on random values tends to cause less randomness. A poster above cited "rand() + rand() + rand() ..." (k times, say) which will in fact tend to k times the mean value of the range of values rand() returns. (It's a random walk with steps symmetric about that mean.)

Assume for concreteness that your rand() function returns a uniformly distributed random real number in the range [0,1). (Yes, this example allows infinite precision. This won't change the outcome.) You didn't pick a particular language and different languages may do different things, but the following analysis holds with modifications for any non-perverse implementation of rand(). The product rand() * rand() is also in the range [0,1) but is no longer uniformly distributed. In fact, the product is as likely to be in the interval [0,1/4) as in the interval [1/4,1). More multiplication will skew the result even further toward zero. This makes the outcome more predictable. In broad strokes, more predictable == less random.

Pretty much any sequence of operations on uniformly random input will be nonuniformly random, leading to increased predictability. With care, one can overcome this property, but then it would have been easier to generate a uniformly distributed random number in the range you actually wanted rather than wasting time with arithmetic.