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Results tagged with pr.probability
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user 57321
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
6
votes
3
answers
2k
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Estimating the variance of a discrete normal distribution
Let $f(x; \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\cdot e^{-\frac{x^2}{2\sigma^2}}$ be the probability density function of a normal distribution $\mathcal{N}(0, \sigma^2)$. We consider a discrete normal …
- 63.9k
2
votes
1
answer
245
views
Asymptotic rate for the expected value of the square root of sample average
I have iid random variables $X_1, \dots, X_n$ with $X_i \geq 0$, $E[X_i]=1$ and $V[X_i] = \sigma^2$.
Let $S_n = \frac{\sum_{i=1}^n X_i}{n}$.
I'd like to say that $E[\sqrt{S_n}] = 1-O(1/n)$.
My first …
- 128k
3
votes
1
answer
682
views
Asymptotic bound on the total variation distance between a standard multivariate normal and ...
Let $P = N(\vec{0}, I^d)$ be a standard multivariate Gaussian distribution in $d$ dimensions. Let $Q$ be distributed the same as $P$, except that samples from $Q$ have one of their coordinates, chosen …
- 128k