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1.2.1 Variable de Bernoulli

Julio Toboso edited this page Jun 1, 2026 · 1 revision

VARIABLE DE BERNOULLI  

Experimento que tiene dos posibles resultados: éxito o fracaso. La variable aleatoria asociada por lo tanto sólo puede adoptar dos Valores: 0 o 1, verdadero o falso, A o B, etc. Normalmente se toma como éxito el 1 y como fracaso el cero.

Parámetro/s que define/n esta variable

  • Probabilidad de éxito: 
    • p= 0.25
Valor
variable
(k)
Función
Probabilidad
$p_X(k)$
$k·p_X(k)$ $k^2·p_X(k)$ Ɛ $Ɛ²·p_X(k)$
0 0.75 0 0 -0.25 0.046875
1 0.25 0.25 0.25 0.75 0.140625
           
𝚺 1 0.25 0.25 0.5 0.1875
𝚺² 1 0.0625 0.0625 0.25 0.03515625
𝚿 0.5 0.125 0.125 0.25 0.09375
𝚫 0.5 0.25 0.25 1 0.09375
𝚸² 0.625 0.0625 0.0625 0.625 0.02197265625
𝚸 0.790569415 0.25 0.25 0.790569415 0.1482317653
       
  Calculada Teórica  
ESPERANZA 0.1 0.1  
VARIANZA 0.09 0.09  
       

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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