## Finite Population Sampling without Replacement

### Personal note of finite population sampling

First moment Population: $$\Omega = \{ x_1, \dots, x_N \}$$ Collection of $n$-samples: $$\mathcal{S} = \{ s \in \Omega^n \mid \forall i,j \in s, i \ne j \}$$ Collection of $n$-samples containing $x$: $$\mathcal{S}_x = \{ s \in \mathcal{S} \mid x \in s \}$$ Observe that $$|\mathcal{S}_x| = \binom{N-1}{n-1}$$. Let population mean be zero. $\mu = 0$, i.e. $$\sum_{i = 1}^N x_i = 0$$ [Read More]

## What are Dataframes?

### Understand dataframes from a non-example

Motivation The books that I read in the past didn't explain what a dataframe meant. Definition Dataframe : A table of data in which the values of each observed variable is contained in the same column. Counterexample I've difficulty in reading long lines of text like the above definition, so let's illustrate this definition with a counterexample. We have carried out repeated experiments with four types of things and obtaine some data. [Read More]

## 2018-10-04 Seminar Notes

I jotted down only a few keywords that might be reusable. I didn't understand any of the talks. Functional Data Analysis Goal: predict equipment temperature Tools: Fourier coefficients (trigo ones), followed by discretisation, min-error estimation, cross-validation 10-folds, $R^2$ adjusted ?, MAE, MSPE Comparison with non-functional data Tolérancement Thème : Traiter les incertitudes sur les dimensions des pièces de l'avion Objectif : établir une modélisation mathématiques construire un virtual twin de l'avion Outils : Modèle de variabilité Modèle d'assemblage \$\text{airbus}: Y = \sum_{i = 1}^n a_iX_i? [Read More]