(Solved): A randam variable, RV: XIt) tos realizatians [epochs) in time-scale, t and the assaciated sutecorr ...

A randam variable, RV: XIt) tos realizatians [epochs) in time-scale, t and the assaciated sutecorrelation function (ACF) is specified as. $ACF?R_{xx}(t,t+T)$ with $T$ being the delay factor (tau). Hence find answers for the questions indicated below with reference to X[t]; and, chocse the correct set of answers in the relevant multiple-thoices listed. Q[a] Given $R_{xx}(t,t+T]?\left[a\times T^2+b\right]/\left(c\times T^2+d\right)$ where $[a,b,c$ and di denotes positive constants. Determine the variance of $X:VXX$, if $a?27,b?33,c?5$ and $d?6$ ) Q(b) Is the process, $X[t]$ in $Q(a)$ stationary? Yes or Na: Why? Q[c] Given $R_{xx}(t,t+T]?[[1?[T)$ for $T?1;$ and, 0 for $T?1\}$. Determine whether the $ACF$ is a valid and $X[t)$ denotes a WSS process (Yes or No; Why?) Q(d) Given Rxoc $(t,t+T)?10\times \sin \left(T^2\right]$. Determine whether the ACF is a valid and $X(t)$ denotes a WSS process (Yes or Na; Why?) Q[e] Given $R_{xx}(t,t+T)?[2??T)$ for $(?1?T?+1)$. Determine whether the $ACF$ is valid and $X(t)$ denotes a WSS process if its expected mesn is constant (Yes or No; Why?) (A randam process is called wide-sense stationary (WSS) if its mean function and its correlation function do nat change by shifts in time. Multiple-choices on the answer-set Choices $Q[a]Q(b)Q(c)Q(d)$ Yes, Valid ACF Yes, Valid ACF No, ACF: Not No, ACF: Not max at Max at T-0. $\begin{array}{llll}10.10& \begin{array}{l}\text{ and constant }\\ \text{ mesn. WSS }\\ \text{ process }\end{array}& \text{ No WSS function }T?0& \text{ Max at }T?0\\ & & \text{ No WSS }& \text{ Even Symmetry }\end{array}$ WSS Process Yes, Valid ACF $\begin{array}{lll}20.12& \text{ Yes: Valid ACF: No; ACF: Not Yes, ACF: Valid }& \\ \text{ No WSS }& \text{ even function WSS Process }& \text{ Max at T-0 }\\ & \text{ Even symmetry }& \end{array}$ Noc, ACF: Not maxx at Nec Nat valid ACF 30.13 Yes; Valid ACF No: ACF: Not $T?0;$ No and WSS even function WSS Process WSS Process Yes, Valid ACF Yes, Valid ACF: No; ACF- Nat Nor, ACF: Nat max at