Random sequence

A random sequence or random sequence generated by the repeated application of a statistical experiment. A random sequence is generally a sequence of realizations of a random variable. The term is mostly used in the sense of a sequence of randomly chosen from a given alphabet or number stock characters.

The simplest random sequence is obtained by a repeated coin toss when one side of the coin, the 0 and the other 1 assigns. It is different random sequences so in a simple 0-1- sequence transcode ( dichotomize ) without the random character is lost.

• Example:

This result was obtained by repeated coin toss. It is striking how often longer, contiguous sequences of 0 or 1 can be found.

A random sequence is characterized by a negligible serial correlation or auto-correlation, that is, the correlation coefficient between successive values ​​in the sequence is not significantly different from zero.

Many naturally occurring time-and location-discrete signals (eg DNA, see DNA sequence analysis ) are statistically analyzed by first postulates the null hypothesis of an underlying random process. Can you refute this hypothesis, ie correlations are in the sequence before, this may have on the sequence of hidden payload back. Especially for dichotomous consequences can check the sequences using the Run tests for randomness, which is labeled " Run" a sequence of identical forms in the sequence. The test will lead to rejection, if too little, but too much runs in a sequence.

True random sequences are, among others, important in the key generation in cryptography.

• Stochastics