Your welcome. Let's try to step back. Here are the major points of the proof:

Ok so

are IID, with distribution given by:

CDF such that F(x) = 0, x <=0.

F(x) = x, 0<x<c and

F(x) = 1 , for x >=c.

THIS IS NOT A CDF IF C>1 since F(x) would not be a non-decreasing function. An RV must be described by a valid CDF. Therefore this problem only makes sense if

since

IS UNDEFINED otherwise (it is defined as a function of ILL-DEFINED components,

. (It

** is** nonsense to discuss

for

, which I say after careful consideration).

So:

Well the expectation of the sum is the sum of the expectations. And the expectation of the product,

**if independent**, is the product of the expectations.

In a previous post, I showed (or tried to show) that

. It is not

because this ignores all of the mass at c.

has a strangeish distribution since the CDF is given by a discontinuous function (for

. This is a very important point that you need to think about. For always continuous functions like we normally work with

since

. The last expression is 0 if

*F* is continuous. But our

*F* is

*not* continuous at c (if

). To compute

you have to mix your approach of continuous and discrete techniques.

So

If

then the fact that

implies that

Also, I didn't mean to imply you were the author. I meant to say either you or the author was saying....