The Gaussian Random Process is completely specified by the mean vector and the autocovariance matrix and hence by the mean vector and the autocorrelation matrix .

(b)  Bernoulli Random Process

A Bernoulli process is a discrete-time random process consisting of a sequence of independent and identically distributed Bernoulli random variables . Thus the discrete-time random process is Bernoulli process if

Example 6

Consider the random sequence generated by repeated tossing of a fair coin where we assign 1 to Head and 0 to Tail. Here is a Bernoulli process where each random variable is a Bernoulli random variable with

•  A sinusoid with a random phase

where are constants and is uniformly distributed between Thus

.