Probability Density Under Transformation
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چکیده
2.1 The Main Theorem We first start with the simplest case where A and B are both subsets of the real line R. Let x ∈ A. The number pA(x) means that, in the infinitesimal interval [x, x+ δx), there exists pA(x)δx amount of “probability mass.” Here, δx is a “differential quantity” such that (δx) = 0. Assume that f is continuous and infinitely differentiable. The function f sends the interval [x, x + δx) to the interval [f(x), f(x+ δx)). By Taylor expansion,
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تاریخ انتشار 2015