2. (10 pt) Find the time-average autocorrelation function and power spectral density of x(t) = 3 + 3 (10π t) + 3 (10π t).

iii) (10pt) Derive the average probability of error based on $ \eta_{\mathrm{MAP}} $ in part ii).Hint: $Q(x) \triangleq \intx^\infty \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} \, \mathrm{d}y$ and $Q(-x) = \int{-\infty}^x \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} \, \mathrm{d}y$.

2. (10 pt) Find the time-average autocorrelation function and power spectral density of \( x(t) = 3 + 3\cos (10\pi t) + 3\sin (10\pi t) \).

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