# Define a sequence of correlated random numbers [ s_{k}=alpha s_{k-1}+(1-alpha) r_{k} ] where (r_{k}) is a unit-variance,

## Question:

Define a sequence of correlated random numbers

\[

s_{k}=\alpha s_{k-1}+(1-\alpha) r_{k}

\]

where \(r_{k}\) is a unit-variance, uncorrelated, Gaussian pseudorandom number while \(0<\alpha<1\) defines the range of the correlations. Show that this sequence is Gaussian distributed, with a zero mean. Determine the variance in terms of \(\alpha\) and compare your result with equation (16.1.2b). Write a code to determine the correlation function (16.1.3). Plot your measured correlation function and compare it to the exact correlation function.

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