L6-S3-Types of Sample Spaces.pdf - Types of Sample Spaces Road Map Key Concepts \u2022 \u2022 \u2022 \u2022 \u2022 Types of Sample Spaces Countable Sample Space

# L6-S3-Types of Sample Spaces.pdf - Types of Sample Spaces...

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Types of Sample Spaces
Road Map Key Concepts Types of Sample Spaces Countable Sample Space Examples Uncountable Sample Spaces Examples Readings Associated Chapter 5 (5.1)
Types of Sample Spaces Recall: A sample space (denoted by S) is the collection of all possible outcomes of the random experiment. Types of Sample Spaces Discrete or Countable Uncountable
Discrete (Countable) Sample Spaces Discrete or Countable each element of the sample space can be arranged and counted one at a time. Example 1: Tossing two coins S = {(H,H), (H,T), (T,H), (T,T)}.
Discrete (Countable) Sample Spaces Discrete or Countable each element of the sample space can be arranged and counted one at a time. Example 2 : Rolling a pair of dice S = 1,1 1,2 1,3 1,4 1,5 1,6 2,1 2,2 2,3 2,4 2,5 2,6 3,1 3,2 3,3 3,4 3,5 3,6 4,1 4,2 4,3 4,4 4,5 4,6 5,1 5,2 5,3 5,4 5,5 5,6 6,1 6,2 6,3 6,4 6,5 6,6
Discrete (Countable) sample Spaces Discrete or Countable each element of the sample space can be arranged and counted one at a time. Example 3 : Observing the number of hits on YouTube a new music video gets. S = {0,1,2,3,4,…}
Types of Countable Sample Spaces -

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Unformatted text preview: Finite Finite • Each element of the sample space can be arranged and counted one at a time. • You will eventually count all the elements in the sample space. Example 1: Tossing two coins S = {(H,H), (H,T), (T,H), (T,T)}. Types of Countable Sample Spaces -Finite Example 2 : Rolling a pair of dice S = 1,1 1,2 1,3 1,4 1,5 1,6 2,1 2,2 2,3 2,4 2,5 2,6 3,1 3,2 3,3 3,4 3,5 3,6 4,1 4,2 4,3 4,4 4,5 4,6 5,1 5,2 5,3 5,4 5,5 5,6 6,1 6,2 6,3 6,4 6,5 6,6 Types of Countable Sample Spaces – Countably Infinite Countably infinite • Each element of the sample space can be arranged and counted one at a time, but • You will never finish counting the elements of the sample space. Example 3 : Observing the number of hits on YouTube a new music video gets. S = {0,1,2,3,4,…} Uncountable Samples Spaces Uncountable – possible outcomes cannot be arranged and counted. Example 4: Observing the final grades (in percentages) of students in resecon212. S = [0, 100]...
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