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Variance of sum of deviations
Suppose I have an i.i.d. sample $\{X_i\}_{i=1}^M$ for some positive integer $M$, and suppose that $X_i \sim X$ for some random variable $X$ with finite variance. Then, denote by
$$
E_M = \frac1M\sum_{...
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Upper bound for Variance of linear combination of random variables: $\operatorname{Var}\left(x^Ta\right) \leq \frac{\|a\|^2}{4}. $
I found this while reading a paper where they used it as a casual fact.
Say, you have a vector $x = (x_1, x_2, \dots, x_n)$ where $x_i \in [0,1]$ are independent random variables. Consider linear ...
- 691
3
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Cramer-Rao Casella Berger 7.38 for exponential family
The question states ''let $X_{1}, \dots, X_{n}$ be random sample from $f(x \mid \theta) = \theta\cdot x^{\theta-1}$ for $0 < x< 1 ; \theta > 0$. Is there a function of $\theta, g(\theta)$ ...
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