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Valid discrete probability distribution examples

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    - [Instructor] Anthony DeNoon
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    is analyzing his basketball statistics.
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    The following table
    shows a probability model
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    for the results from his
    next two free throws.
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    And so he has various outcomes
    of those two free throws,
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    and then the corresponding probability.
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    Missing both free throws, 0.2.
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    Making exactly one free throw, 0.5.
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    And making both free throws, 0.1.
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    Is this a valid probability model?
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    Pause this video and see if you
    can make a conclusion there.
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    So let's think about what makes
    a valid probability model.
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    One, the sum of the probabilities
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    of all the scenarios
    need to add up to 100%.
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    So we would definitely want to check that.
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    And also, they would all
    have to be positive values
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    or I guess I should say none
    of them can be negative values.
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    You could have a scenario
    that has a 0% probability.
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    And so all of these look
    like positive probabilities,
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    so we meet that second test
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    that all the probabilities
    are non-negative,
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    but do they add up to 100%?
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    So if I add .2 to .5, that is .7,
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    plus .1, they add up to 0.8
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    or they add up to 80%.
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    So this is not a valid probability model.
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    In order for it to be valid,
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    they would all, all the various scenarios
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    need to add up exactly to 100%.
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    In this case, we only add up to 80%.
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    If we add it up to 1.1 or 110%,
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    then we would also have a problem.
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    We can just write no.
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    Let's do another example.
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    So here we are told you are a space alien.
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    You visit planet Earth
    and abduct 97 chickens,
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    47 cows, and 77 humans.
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    Then you randomly select
    one Earth creature
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    from your sample to experiment on.
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    Each creature has an equal
    probability of getting selected.
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    Create a probability model to show
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    how likely you are to select
    each type of Earth creature.
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    Input your answers as fractions
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    or as decimals rounded
    to the nearest hundredth.
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    So in the last example, we wanted to see
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    whether the probability model
    was valid, was legitimate.
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    Here, we wanna construct a
    legitimate probability model.
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    Well, how would we do that?
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    Well, the estimated probability
    of getting a chicken
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    is gonna be the fraction
    that you're sampling from
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    that is our chickens because
    any one of the animals
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    are equally likely to be selected.
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    97
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    of the 97
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    plus 47
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    plus 77 animals are chickens.
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    And so what is this going to be?
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    This is gonna be 97 over.
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    97,
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    47, and 77,
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    you add 'em up.
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    Three sevens is a 21.
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    And then let's see, two plus nine is 11,
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    plus four is 15,
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    plus seven is 22,
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    so 221.
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    So 97 of the 221 animals are chickens.
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    And so I'll just write 97, 221s.
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    They say that we can answer as fractions,
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    so I'm just gonna go that way.
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    What about cows?
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    Well, 47
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    of the 221 are cows,
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    so there's a 47, 221st probability
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    of getting a cow.
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    And then last but not least,
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    you have 77 of the 221s are human.
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    Is this a legitimate
    probability distribution?
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    We'll add these up.
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    If you add these three fractions up,
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    the denominator's gonna be 221
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    and we already know that
    97 plus 47 plus 77 is 221.
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    So it definitely adds up to one,
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    and none of these are negative,
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    so this is a legitimate
    probability distribution.
Title:
Valid discrete probability distribution examples
Description:

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Video Language:
English
Team:
Khan Academy
Duration:
04:00

English subtitles

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