If (x(t)=x_{1}(t)-2 x_{1}(t-5)+x_{1}(t-10)), determine the autocorrelation functions (mathfrak{R}_{x_{1}}(t)) and (mathscr{R}_{x}(t)) when (x_{1}(t)=exp left(-t^{2} / 2ight)).

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If \(x(t)=x_{1}(t)-2 x_{1}(t-5)+x_{1}(t-10)\), determine the autocorrelation functions \(\mathfrak{R}_{x_{1}}(t)\) and \(\mathscr{R}_{x}(t)\) when \(x_{1}(t)=\exp \left(-t^{2} / 2ight)\).

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