What is Deterministic and random signals
A signal can be said as deterministic if there is no uncertainty with respect to its value at any time or as random. That means that there is some degree of uncertainty before the signal occurs. Deterministic signals are modeled by explicit mathematical expressions. For a random waveform it is not possible to wire  such an explicit expression. However, it may exhibit certain regularities that can be described in terms of probabilities and statistical averages. Such a model, in the form of a probabilistic description of the random process is particularly useful for characterizing signals and noise in communication systems.
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What is Deterministic and random signals
A deterministic signal is the kind of signal where each value of the signal is fixed and can be determined by a mathematical expression, a rule, or a table. Because of this characteristic, the signal’s succeeding values can be calculated from previous values with high assurance.
A random signal is the total opposite of the deterministic signal. Its behavior has a lot of improbability and its future values can hardly be predicted. Literally, the future values cannot accurately be calculated and can usually only be guessed based on the averages of sets of signals. See the diagram below for your reference. To learn the different classifications and properties of signals, you may visit Connexions® | Signal Classifications and Properties.