# Tagged Questions

Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component.

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### Dice roll, estimator, epsilon

We roll a non-symmetric die. Let $X_n$ be the reulst of $n$-th roll. $$P(X_n = 6)= \frac{1}{6} + \varepsilon, \ P(X_n = 1) = \frac{1}{6} - \varepsilon, \ P(X_n=2) = ... = P(X_n = 5) = \frac{1}{6}$$ ...
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### Unbiased estimator for the sum of numbers

Let $\alpha_1, \dots, \alpha_n \in \mathbb{R}$. We want to approximate the sum as follows $$S = \sum_{i=1}^{n} \alpha_i \approx \dfrac{n}{c} \sum_{i=1}^{c} \alpha_i,$$ where $\alpha_i$ is picked ...
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### How to find out the control function of a cosine wave?

I have a system which is sampling at 100Hz. There is only one input for the system. The output is similar to cosine waveforms with varying frequency. I have no clue how to find out the exact formula ...
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### expected 1 norm of a normal vector

Given a normal vector $X$ such that $\mathbb{E}(X)=0$ and $Cov(X)=Id$, is it possible to get an expression for $$\mathbb{E}(\|A X\|_1)$$ where $A$ is a given matrix. I know that in dimension 1, we ...
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