GATE EC 2015 Set 2 Q50 — Probability and Statistics

$\begin{Bmatrix} X_{n}\\ \end{Bmatrix}_{n=-\infty}^{n=\infty}$ is an independent and identically distributed (i.i.d.) random process with ܺ$X_{n}$ equally likely to be $+1$ or $−1.\:\:\begin{Bmatrix} Y_{n}\\ \end{Bmatrix}_{n=-\infty}^{n=\infty}$ is another random process obtained as ܻ$Y_{n}=X_{n} + 0.5X_{n-1}.$ The autocorrelation function of $\begin{Bmatrix} Y_{n}\\ \end{Bmatrix}_{n=-\infty}^{n=\infty},$ denoted by $R_{Y}[k],$ is