Math 2.0

definition

Sample space

Definition

Let EE be a random experiment. A sample space of EE is a nonempty set Ω\Omega with two properties. Each performance of EE gives exactly one element of Ω\Omega. Each element of Ω\Omega is a possible result of EE. The usual notation for a sample space is Ω\Omega or SS.

Remarks

The elements of Ω\Omega are mutually exclusive: two different elements cannot both be the result of one trial. They are also collectively exhaustive: some element is always the result. For one toss of a coin, Ω={H,T}\Omega = \{H, T\}. For two rolls of a die, Ω={1,…,6}2\Omega = \{1, \dots, 6\}^2 has 3636 elements. One experiment can have more than one sample space. For a card drawn from a deck, Ω\Omega can be the set of 5252 cards or the set of the 44 suits. A sample space can be finite, countably infinite or uncountable. The time until a lamp fails has the sample space [0,∞)[0, \infty).

Explanations

L1 human

The sample space is the list of everything that can happen in the experiment. For a die, the list is 1,2,3,4,5,61, 2, 3, 4, 5, 6. Every question about the die is then a question about this list.

What this node needs for W2
  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

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171 nodes use this node, directly or through other nodes.

Sources

  1. Web https://en.wikipedia.org/wiki/Sample_space, Conditions of a sample space

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