Re: PULSE INTEGRATION
actually it is good question. To answer it accurately, you need to find what is the value of an accumulated gaussian randon variable, given the mean and variance of the distribution. I think the answer is that the accumulated sum is also gaussian.
In the context of your problem, you cannot assume that the noise accumulates to zero, only the average wil be nearly zero. The sum is still a gaussian random variable.
Of course, if your signal is also zero mean and periodic (as a sine is) it will also accumulate to zero, determinstically. In short, averaging is not a good idea in this context. correlation would be much better.
-b