jesterII
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 Apr15 comment Abuse of notation in declaring a variable is a function of another? This is an intersting idea; how does $y = y \circ id_{X}$ solve the problem? Are you saying that $y$ is a function on the both sides, and that $y(x) = (y \circ id_X) (x)$ for all $x$ (i.e is this a statement of equivalence, rather than assignment)? Apr14 comment Notation for a statistic, or function of a random variable Thank you. This is a point which confuses me to no end in the literature. I usually can understand the author's meaning from context, but when thinking formally about the underlying mathematical objects I end up hopelessly lost. Apr14 accepted Notation for a statistic, or function of a random variable Apr13 comment Notation for a statistic, or function of a random variable Does that mean $S$ is not a statistic? It is a function on real numbers, not random outcomes. Apr13 asked Notation for a statistic, or function of a random variable Apr4 comment 3 Variables, One Equation Try this idea: $x(x-7) + y(y-7) + z(z-7) = 0$. This has 56 integer solutions. Its a sphere. Apr3 accepted Abstract Integration in Elementary Probability Theory Apr3 comment Abstract Integration in Elementary Probability Theory Thank you. I understand the technical definitions of integration of $X$ with respect to $\mathbb{P}$. When $X$ has a density $f$, the expectation $\int_{x \in Im(X)} x f(x)dx$ is commonly explained as a weighted sum of the values $x$ that $X$ can take, where the value $f(x)dx$ is the probability that $X$ is in the neighborhood of $x$, or approximately $\mathbb{P}(X \in [x, x+dx])$ Apr2 asked Abstract Integration in Elementary Probability Theory Mar20 suggested rejected edit on General Solution to a Specific Problem Mar20 answered General Solution to a Specific Problem Mar19 revised General Solution to a Specific Problem mathjax rather than html Mar19 suggested approved edit on General Solution to a Specific Problem Mar18 comment General Solution to a Specific Problem OK, can you share your ideas as to how you derived $P(X=x)$? It is not correct as written. Mar18 comment General Solution to a Specific Problem is this a homework problem? Mar11 comment Interpreting the expected value as an abstract integral? Spelling mistake. Mar11 revised Interpreting the expected value as an abstract integral? deleted 4 characters in body Mar11 accepted Interpreting the expected value as an abstract integral? Mar11 asked Interpreting the expected value as an abstract integral? Feb20 comment Mathematical justification for incorporating a conditional event in expectation? This is a great answer. In particular, expressing the random variable $g(N) = I_k(N)$, and the equality in step 3, were profoundly insightful.