# Tagged Questions

For mathematical proofs or derivations of results.

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I'm working through Convolutional Neural Network paper here on adversarial learning and I'm having trouble with the derivative proof of adversarial logistic regression. The correct answer presented (...
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### datav alidation on lexcel [closed]

I have given data validation for Std. warehouse as "YGCTCAP1" and "YGCTBAP1" for the first row i entered YGCTCAP1 by drop down, and i drag down the cell, it in became YGCTCAP2, --3,--4 ETC , ...
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### median proof given G(t)=F(t-delta) [closed]

How can I do part a? I get stuck after using the formula for difference of 2 independent variable
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### regression sum of squares in multiple linear regression

I'm looking for some help with the following practice question for an upcoming midterm:
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### Proof for probability of union of n events

I'm trying to refresh my knowledge of probability so I'm working my way through Haigh's Probability Models 2e. I'm looking at one of the corollaries presented (1.3) and I don't understand it. The ...
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### Naive Bayes Derivation

I was going over the derivation of Naive Bayes, and the following 3 lines were given: Suppose $X = \left < X_1, X_2 \right>$ \begin{align} P(X|Y) &= P(X_1, X_2 | Y) \\[2pt] &= ...
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### Looking for proof of conditional dependence, when the conditioning variables are linearly related

Suppose we have three random variables, $X$, $Y_1$, and $e$ (for error). Variable $e$ is independent of $X$ and $Y_1$, but $X$ and $Y_1$ are dependent. Further suppose we construct a new mixture ...
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### Proving a property of $(n-1)s^2$

I would appreciate your help as I climb the stats learning curve! I want to prove the following: "Let $x_1, x_2, ... , x_n$ be any numbers and let $\overline x = (x_1 + x_2 + ... + x_n)/n$ Then ...
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### How do I prove that using OLS on de-meaned data gives the same estimates as using a dummy variable regression?

I obtained the FOCs for the dummy variable regression and know that I have to manipulate them to get the FOCs for the regression on the de-meaned data but am not sure how to go about it, as in how to "...
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### Bayesian inference for the rate parameter $\lambda$ of an exponential with Accept Reject

Let a prior distribution be $$\pi(\lambda)=\begin{cases} \frac{2\lambda}{3} & 0 < \lambda \le 1 \\ \frac{2}{3\lambda^2} & \lambda > 1 \end{cases}$$ This ...
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### Modeling a time series - help in understanding the approach in a paper

The question is based on a paper titled : Forecasting high waters at Venice Lagoon using chaotic time series analysis and nonlinear neural networks On page 2 right above Eq(1), the authors say ...
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### Proof of almost deterministic random variables [closed]

Let $X$ and $Y$ be independent random variables and suppose that $P(X + Y = c) = 1$, where $c \in \mathbb{R}$ is a constant. Prove that $X$ and $Y$ are both almost deterministic random variables (...
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### ARCH(âˆž) = GARCH(p,q) proof

I am aware that the similiar question was asked already here. However, I read Bollerslev (1986) and I struggle hard with the rearrangements and substitutions he makes. Hence, there are subquestions to ...
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### What is my missing assumption is sum of variances?

In this answer, it says that in general the sum of the variances is not equal to the variance of the sum. I tried to work it out by myself, and I think I got a different result, namely that the ...
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### Help with a proof of Bayes classifier optimality

I have a class assignment to provide a proof that Bayes classifier for the two label version is optimal in that it's error rate is always ${\le}$ any other classifier. I've never worked through a ...
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### Clustering — Intuition behind Kleinberg's Impossibility Theorem

I've been thinking about writing a blog post on this interesting analysis by Kleinberg (2002) that explores the difficulty of clustering. Kleinberg outlines three seemingly intuitive desiderata for a ...
### Prove that the event '$\lim Y_n$ is finite' is in the tail $\sigma$-algebra of $Y_1, Y_2, …$
Given random variables $Y_1, Y_2, Y_3, ...$, let $\tau = \bigcap_{m\geq1} \sigma(Y_{m+1}, Y_{m+2}, ...)$ be their tail sigma-algebra. For convenience, $\tau_m \doteq \sigma(Y_{m+1}, Y_{m+2}, ...)$. \$...