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The response of a discrete time system $y[n]$ obeys the following relation:

\[
y[n]=\frac{5}{6} y[n-1]-\frac{1}{6} y[n-2]+x[n] .
\]

The input to the system is $x[n]=\delta[n]-\frac{1}{3} \delta[n-1]$.

Which of the following options is TRUE for $y[n]$?

  1. Stable and causal response
  2. Stable and non-causal response
  3. Unstable and causal response
  4. Unstable and non-causal response

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