Question shown in picture. Please provide mathematical proof.

2. Stationarity and systems: show that a. the output of a memoryless system to a strict-sense stationary (SSS) process input is strict sense stationary. b. the output of a memoryless system to a WSS process input may not be a WSS. c. the output of a linear time invariant (LTI) system to a wide-sense stationary (WSS) process input is again wide sense stationary. d. The output of a LTI system to a SSS process input is again SSS. e. The output of a linear system to a Gaussian process is again Gaussian