# Meaning of “choose a random thing independently”

a random walk chooses a random bit independently and it moves left or right if the bit chosen is 0 or 1, respectively.

I was wondering if "choose a random bit independently" means that the random bit has a uniform distribution over {0,1}, and the walk sample this uniform distribution?

I remember that I often see expression such as "choose a random thing independently". Does it mean the random thing has a uniform distribution over its range? Does it have something to do with independence between events or random variables?

• I think in this context it means each bit is independent of the previous ones. But this is not correctly formulated. – Elvis Dec 6 '12 at 15:56