Define Sample Space

Discussion in 'Probability and Statistics' started by nycmathguy, Jul 6, 2021.

  1. nycmathguy

    nycmathguy

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    In basic terms, define a sample space. Give an easy example using the sample space idea.

    Thanks
     
    nycmathguy, Jul 6, 2021
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  2. nycmathguy

    MathLover1

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    Simply, a sample space is the range of values of a random variable.
    or
    The collection of all possible outcomes of a probability experiment forms a set that is known as the sample space.

    Definition: random experiment
    A random experiment is a mechanism that produces a definite outcome that cannot be predicted with certainty. The sample space associated with a random experiment is the set of all possible outcomes. An event is a subset of the sample space.

    Definition: Element and Occurrence

    An event E is said to occur on a particular trial of the experiment if the outcome observed is an element of the set E .

    Example 1: Sample Space for a single coin

    Construct a sample space for the experiment that consists of tossing a single coin.

    Solution

    The outcomes could be labeled h for heads and t for tails. Then the sample space is the set: S={h,t}




    Example 2 : Sample Space for a single die

    Construct a sample space for the experiment that consists of rolling a single die. Find the events that correspond to the phrases “an even number is rolled” and “a number greater than two is rolled.”

    Solution:

    The outcomes could be labeled according to the number of dots on the top face of the die. Then the sample space is the set S={1,2,3,4,5,6}
    The outcomes that are even are 2,4,and6 , so the event that corresponds to the phrase “an even number is rolled” is the set {2,4,6} , which it is natural to denote by the letter E . We write E={2,4,6} .

    Similarly the event that corresponds to the phrase “a number greater than two is rolled” is the set T={3,4,5,6} , which we have denoted T .

    A graphical representation of a sample space and events is a Venn diagram:
     

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    MathLover1, Jul 6, 2021
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  3. nycmathguy

    nycmathguy

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    Perfect but like you suggested, I will put a hold on probability for now. No sense in learning two courses simultaneously.
     
    nycmathguy, Jul 6, 2021
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  4. nycmathguy

    MathLover1

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    learning two courses simultaneously is only for the student enrolled in undergraduate mathematics major
     
    MathLover1, Jul 6, 2021
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  5. nycmathguy

    nycmathguy

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    Exactly. This is not my case. Leaving probability for the future.
     
    nycmathguy, Jul 7, 2021
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