This paper presents some results about transformations of infinite random sequences by letter to letter rational transducers. We show that it is possible by observing initial segments of a given random sequence to decide whether two given letter to letter rational transducers have the same output on that sequence. We use the characterization of random sequences by Kolmogorov Complexity. We also prove that the image of a random sequence is either random, or non-random and non-recursive, or periodic, depending on some transducer's structural properties that we give.