Stratified Sampling from the Negative Exponential Distribution

I have tried to present a thorough investigation into the problem of stratified sampling under the assumption of a given population the negative exponential distribution. The methods and simplifications herein presented are, I feel, both statistically around and feasible in application. The extension of stratified sampling for a particular distribution, I believe, has definite advantages over no such assumption. This is particularly true for the highly skewed distributions such as herein discussed