# Tagged Questions

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### How to compute bounding coefficients for McDiarmid's inequality?

I am trying to understand the proof in Sec. A2 of Gretton et al.. To make the question self-contained, I summarize below the key ingredients. At the end of the post, I state my question. Given a ...
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### Layman explanation of Cramér–Rao bound [closed]

I am trying to understand Cramér–Rao bound, but I have a problem understanding the formula in Wikipedia. Can somebody tell me the intuitive way of it?
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### Arithmetic minus geometric means and the coefficient of variation

This question inspires a further question: For a probability distribution supported on the positive half-line, is the difference between the arithmetic and geometric means bounded by some known ...
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### Probability than empirical mean of one binomial RV smaller than another

Lets suppose I have two binomial random variables: $X \sim B(n_1, p_1)$ and $Y \sim B(n_2, p_2)$. I would like to calculate the probability than the empirical mean of $X$ be smaller than the empirical ...
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### Express similarity measure in terms of probability

I am trying to express similarity measures between objects in 2 sets. Below are the details of my measures. 1) Compare object - 1 with all the objects in set-2 (object - (2-9)). 2) Similarity measure ...
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### Empirical Bernstein Bound for distributions outside range(0,1)

I'm working on using empirical Bernstein bounds to estimate the mean difference between 2 variables from different distribution. The algorithm samples from each variable until it detects a ...
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### If distance correlation $DCOR(X,Y) = 0.5$ then are X and Y dependent or independent?

If distance correlation $DCOR(X,Y) = 0.5$ then are $X$ and $Y$ statistically dependent or independent? What about when $DCOR(X,Y) > 0$, are they statistically dependent for sure even when it's less ...
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### Binomial and Poisson issues (Jacod and Potter)

I've been reading through Probability Essentials by Jacod and Potter (2nd edition). I'm on a voyage to do every single exercise in the book. The following problems I am unsure of is as such: 5.11) ...
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### About calculating the marginal PDFs from a joint PDF [duplicate]

I am trying to find the marginal distributions of a given joint probability density function. The joint density is $f(x,y) = xe^{-x(y+1)}$ for $x$ and $y$ positive and zero everywhere else. If I have ...
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### Distribution of a transformation of a random variable

I have started off by this: $F_Y(Y)=P(Y\leq y)=P(X^2 \leq y).$ Now, I have been told that $P(X^2 \leq y) = P(- \sqrt y \leq X \leq \sqrt y)$. I don't quite understand why this is and any help would ...
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### Better Moment Inequalities

How do you determine if a moment inequality is better than another? Say for example, compare the Chebyshev's inequality with this nameless inequality where P{|X|≥ Kσ} ≤ (μ4-σ4)/(μ4+K4σ4-2K2σ4). I ...
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### Dvoretzky–Kiefer–Wolfowitz inequality hold for discrete distributions?

I am wondering whether Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions? Any comments or references would be greatly appreciated.
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### bound on expectation of a two-variable function under an independent distribution

Consider a probability distribution $P(x)$, a set observed samples $S = \{x_1,\cdots, x_n\}$ where $x_i \stackrel{iid}{\sim} P(x)$ for $i \leq n$, and a symmetric function $h(x,y)$. How can one ...
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### How to combine probability inequalities that are w.r.t. different random variables?

Let $x$ and $z$ be two independent random variables. Suppose I know the following two facts: $P_z[f(x,z) < g(x)] > 1-\delta$ uniformly for all x; $P_x[g(x) < h(x)] > 1-\delta_h$ How can ...
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### Probability inequality implication

Let $X$ and $Y$ be independent random variables, and $A(X,Y)$ a predicate with values true or false. Suppose we know the following: $P_Y[\forall X, A(X,Y) \Rightarrow B(X)] > 1-\delta$. Can we ...
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### $E(X)E(1/X) \leq (a + b)^2 / 4ab$

I've worked on the following problem and have a solution (included below), but I would like to know if there are any other solutions to this problem, especially more elegant solutions that apply well ...