Recent content by robbins

This solution was posted by Joseph Wright on LaTeX Community: "You don't want \let, you want to do things with numbers proper. The thing is that they then [need] to be assigned to TeX counters. You seem to want something like \newcount\mycount \newenvironment{foo}[1] {% \mycount...

How can I increment or decrement a parameter in LaTeX? For example, suppose I create an environment [FONT="Courier New"]foo as follows: [FONT="Courier New"]\newenvironment{foo}[2]{\begin{tabular}{*{#1}c*{#2}r}}{\end{tabular}} I can write [FONT="Courier New"]\begin{foo}{4}{3}...

This is not homework. Case I is mostly for background. The real questions are in Case II. Case I (one dimension): a. Suppose X is a continuous r.v. with pdf fX(x), y = g(x) is one-to-one, and the inverse x = g-1(y) exists. Then the pdf of Y = g(X) is found by f_Y(y) = f_X(g^{-1}(y) |...

Your interpretation is correct. My original question was not stated clearly (should have used subscripts).

A space-filling curve is everywhere self-intersecting, and therefore can't be injective (though they are surjective). However, your point is taken: by Cantor's theorem the cardinality of [0, 1] is the same as [0, 1]^n for any finite n. And a mapping f : A -> B where |A| = |B| can be injective.

Q1. Claim: Suppose f : Rn -> Rm is injective. Then m >= n. Is this true? Q2. Claim: Suppose f : Rn -> Rn is injective and f(X) = [f1(X) f2(X) ... fn(X)]T. Then each fk must be injective. Is this true? Q3. I assume the above claims are known results or have known counterexamples. Can...

Let the random variable X have the probability density function f(x). Suppose f(x) is continuous over its domain and Var[X] is bounded away from zero: 0 < c < Var[X]. Claim: f(x) is bounded over its domain. Is this claim true? I don't think a counterexample like X ~ ChiSq_1 applies...