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1.2.3. Variable Uniforme

Julio Toboso edited this page Jun 1, 2026 · 3 revisions

VARIABLE ALEATORIA UNIFORME

Experimento consistente en elegir un valor dentro de un conjunto dado y finito de valores. No hay preferencia sobre ninguno de ellos, por lo tanto la probabilidad de que salga cualquiera de ellos es la misma.

Parámetro/s que define/n esta variable

Número de elementos

  • $L = 10$
Valor
variable
(k)
Función de
Probabilidad
$p_X(k)$
$k·p_X(k)$ $k²p_X(k)$ $Ɛ²$ $Ɛ²·p_X(k)$
1 0.1 0.1 0.1 -5.4 2.916
2 0.1 0.2 0.4 -5.3 2.809
3 0.1 0.3 0.9 -5.2 2.704
4 0.1 0.4 1.6 -5.1 2.601
5 0.1 0.5 2.5 -5 2.5
6 0.1 0.6 3.6 -4.9 2.401
7 0.1 0.7 4.9 -4.8 2.304
8 0.1 0.8 6.4 -4.7 2.209
9 0.1 0.9 8.1 -4.6 2.116
10 0.1 1 10 -4.5 2.025
           
         
𝚺 1 5.5 38.5 -49.5 24.585
𝚺² 1 30.25 1482.25 2450.25 604.422225
𝚿 0.1 0.55 3.85 -4.95 2.4585
𝚫 0 0.9 9.9 0.9 0.891
𝚸² 0.1 3.85 253.33 245.85 61.251333
𝚸 0.316227766 1.962141687 15.9163438 15.67960459 7.826323083
           
         
  Calculada Teórica      
ESPERANZA 5.5 5.5      
VARIANZA 8.25 8.25      

Data

Legend:

  • 🔰 Start here
  • 🏵️ Important Insight
  • ⚙️ Technical and applications
  • 💻 Some Code
  • ⚜️ Advanced Topics

Start

01 · Ω — What could happen

02 · X, 𝒳 — What we observe

03 · p(x) — What we expected

04 · I(x), H(X) — What an observation tells us

05 · Data — What is consistent

06 · Statistics — What we can learn.

07 · Databases - How to store data

08 · μ(x) — Fuzzy - When data is flexible

  • 08.1 Fuzzy Logic (planned)
  • 08.2 Fuzzy Numbers (planned)
  • 08.3 Possibility vs Probability (planned)

09 · x(t) — Signals and systems - Where patterns live

  • 09.1 Signals (stub)
  • 09.2 Sampling and Aliasing (planned)
  • 09.3 Convolution (planned)
  • 09.4 Frequency (planned)

10 · f_θ — Modelling and linear algebra

  • 10.1 🔰 Vectors and Matrices (planned)
  • 10.2 Mathematical Modelling (planned)

11 · min L(θ) — Optimisation

  • 11.1 🔰 Derivatives (planned)
  • 11.2 Convex Optimisation (planned)

12 · Learning from data

13 · Cause, design, capstone

  • 13.1 Cause and Effect (planned)
  • 13.2 Capstone Guide (planned)

Appendix

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