There are 2 questions dealing with discrete variables I have included as attachment which I hope someone could help shed some light on.

For Question 1, what exactly is a discrete variable Z? All I observe is with each increment of Z, it is effectively the equivalent of integrating the exponential function of T with Z as the upper limit and (Z-1) as the lower limit. So how should I define this discrete variable Z as defined in the question?

For Question 2, could someone show how T.exp(alpha) is an exponential random variable with parameter lamda?

Thanks.