A Statistical Proof of the Transformation Theorem
Posted: 19 Mar 2012
Date Written: March 17, 2012
The well-known transformation theorem (or change-of-variables theorem) is difficult to prove, requiring knowledge of theorems in advanced analysis. For this reason, it is stated without proof in all the statistics textbooks we know of. Here, we provide a new and much simpler proof, by exploiting the fact that it is a density function which is being transformed, and the idea of conditioning.
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