All Questions
6
questions
0
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1
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58
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Bounds on the ratio between second raw moment and expected of absolute value squared
I'm interested in bounds for the ratio $E[X^2]/E[|X|]^2$. The best lower bound is $1$ since $E[|X|] \geq E[X]$ and $E[X^2] - E[X]^2 = Var(X) \geq 0$. On the other hand, I would like to know if there ...
- 63
0
votes
1
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58
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Bound on the expected time of first success in a series of Bernoulli RVs
Given an infinite series of Bernoulli RVs $X_1,X_2,...$ (which may be differently distributed and mutually dependent), we are given that for every $n>0$, $$\mathbb{E}\left[\sum_{t=1}^{n}(1-X_t)\...
- 47
15
votes
1
answer
204
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Show that $\mathbb{E}\left|\hat{f_n}-f \right| \leq \frac{2}{n^{1/3}}$ where $\hat{f_n}$ is a density estimator for $f$
Question
Suppose we have a continuous probability density $f : \mathbb{R} \to [0,\infty)$ such that $\text{sup}_{x \in \mathbb{R}}(\left|f(x)\right| + \left|f'(x)\right|) \leq 1. \;$ Define the ...
- 153
1
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0
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41
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Nice bounds for 3rd folded central moment in terms of variance?
Say we have some real numbers $x_1, \ldots, x_n$, and let $\mu$ be their mean and $\sigma^2$ be the variance. Are there some nice bounds for $\frac 1n \sum_{i=1}^n |x_i - \mu|^3$ based on $\sigma^2$? ...
- 8,945
1
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0
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55
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Showing that the following ratio expectation is bounded by $O(1/n)$
Suppose that $V_i$, $i \in \mathbb{N}$ are i.i.d. standard normal random variables and let $Y_i = \sum_{k=1}^i V_i$ for $i\geq 1$ and $Y_0 = 0$. Consider the following ratio random variable
$$R = \...
- 1,180
3
votes
1
answer
81
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The expected weight-ratio between weighted and un-weighted balls when picked from a bin without replacement
The Problem
The problem, I believe, can be stated in the following way: Given $K$ white balls all with without weight (one can say that the weight is $0$) and $N - K$ red balls with individual ...
