Problem 4. [10 pts] For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear, and (4) time invariant.
(a) $y[n] = \cos(\pi n)x[n]$
(b) $y[n] = x[n^2]$
(c) $y[n] = x[n] \sum_{k=0}^{\infty} \delta[n - k]$
(d) $y[n] = \sum_{k=n-1}^{\infty} x[k]$
