What are the definitions of memoryless, linear, and stable properties?

[nacho-man]

Hi, I need to prove/disprove the following statements. I am facing lots of difficulty though. Intuitively my guess is that they are all true, but I cannot begin to think how I would prove them.

I have attached the questions and appreciate any help.

Thanks.

 

[Opalg]

You need to apply the definitions of these properties. What are the definitions of memoryless, linear, stable?