1. For each of the following discrete-time systems, characterize if the system is memoryless, causal, invertible, BIBO stable, time-invarying (TI), or linear.\
a. $y[n] = \frac{1}{3}(x[n] + x[n - 1])$.\
b. $y[n] = n^2x[n]$.\
c. $y[n] = x[[n]]$.\
d. $y[n] = x[n] - x^2[n - 1]$.\
Note that: for each of these systems you need to argue/show why any given property holds or not.