Bifalgorithm post · Brisk · Chapter 1

What are outcomes and sample spaces?

What are outcomes and sample spaces? (Brisk · Chapter 1) — "Since life is uncertain, we don’t know for sure what is going to happen. But let’s start by assumin…

Ideas in this flowchart

  • El espacio muestral reúne todos los resultados posibles de una situación incierta.
  • La vida es incierta, por lo que no sabemos con seguridad qué ocurrirá.
  • Un resultado es una forma posible en que puede terminar un acontecimiento.
  • Un resultado puede entenderse como el resultado de un experimento, aunque no tiene que haber sido manipulado y medido científicamente.
  • Ω, el espacio muestral, es el conjunto de todos los resultados posibles.
  • Ω también representa el dominio de discurso, el conjunto universal o todo aquello de lo que se habla.
  • Cualquier resultado particular o es un elemento del espacio muestral.
  • Cada situación puede definirse mediante un conjunto específico de resultados posibles.
  • Para un nacimiento, Ω = {niño, niña}; cada nacimiento produce uno de los dos resultados.
  • Para lanzar un dado, Ω = {1, 2, 3, 4, 5, 6}.
  • Para un viaje por carretera, Ω = {seguro, accidente}.
  • Los resultados de un espacio muestral no tienen que ser igualmente probables.
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What are outcomes and sample spaces?

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Brisk

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"Since life is uncertain, we don’t know for sure what is going to happen. But let’s start by assuming we know what things might happen. Something that might happen is called an outcome. You can think of this as the result of an experiment if you want to, although normally we won’t be talking about outcomes that we have explicitly manipulated and measured via scientific means. It’s more like we’re just curious how some particular happening is going to turn out, and we’ve identified the different ways it can turn out and called them outcomes. Now we’ve been using the symbol Ω to refer to “the domain of discourse” or “the universal set” or “all the stuff we’re talking about.” We’re going to give it yet another name now: the sample space. Ω, the sample space, is simply the set of all possible outcomes. Any particular outcome — call it O — is an element of this set, just like in chapter 1 every conceivable element was a member of the domain of discourse. If a woman is about to have a baby, we might define Ω as { boy, girl }. Any particular outcome o is either boy or girl (not both), but both outcomes are in the sample space, because both are possible. If we roll a die, we’d define Ω as { 1, 2, 3, 4, 5, 6 }. If we’re interested in motor vehicle safety, we might define Ω for a particular road trip as { safe, accident }. The outcomes don’t have to be equally likely, an important point we’ll return to soon."

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