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Probability

  • What does a Geometric random variable become after sampling some coffee without replacement?

    Answer: A Hypergeometric variable!

    Sara Venkatraman

  • How many statisticians does it take to change a light bulb?

    Answer: That depends on the model

    Robert Weiss

  • lyric © 2017 Lawrence M. Lesser
    sing to the tune of “Every Breath You Take” (Sting)

    For a two-man game
    where chances are the same.
    to win each frame,
    you just play the game to a score agreed to.

    If you take a break,
    divvy up the stakes.
    For fairness’ sake,
    you may only take what is due to you.

    Now we did see  in 17th-century: 
    Pascal and Fermat gave  a solution they made

    Well, their letters say
    just how many ways
    the unfinished frames 
    could have been played and how odds accrue.

    Problem solved, thanks to Pascal and Fermat,
    but there is more that their answer did unlock:
    Just look around at the theory that we use
    of probability and its allied tools.
    Let’s rejoice this problem of the points…….

    Divvy up the stakes
    for an unfinished game:
    For fairness’ sake,
    you may only take what is mu for you.


  • lyric © 2017 Lawrence M. Lesser
    may sing to the tune of “Material Girl” (Peter Brown and Robert Rans, popularized by Madonna)

    Data values  normally are 
    no more far away
    Than 3 standard  deviations  
    from the mean displayed.
    And within 2 deviations, 19 of 20 lie, that’s right!
    And within 1  deviation,  2/3 are confined,  

    CHORUS:
    ‘Cause we are living in an empirical world
    and I need an empirical tool.
    You know that we are living in an empirical world
    and I use the empirical rule!

    If I think a  population
    looks bell curve to me,
    The rule helps tag outliers like a
    z-score more than 3.
    But if the population may not
    take the normal shape (no way!),
    Frequencies that  you expect can
    help you ascertain 

    (Repeat Chorus)

  • Music and Lyrics © 2016 Greg Crowther

    The sample means have a normal distribution
    Even if the population does not.
    Their center is the center of the population.
    When this is true, you can sure do a lot.

    CHORUS:
    Whoa-oh-oh-oh, Central Limit Theorem
    For populations with finite variance and mean.
    If you know-oh-oh-oh the samples are  independent 
    And distributed identically: that's a stat person's dream.

    The further that the population is from normal,
    The larger that your sample size must be.
    If you're sampling Chicago household incomes,
    Sample lots of them to use the CLT!

    [REPEAT CHORUS] 
  • Q: How do you model how an athlete's weight relates to the severity of a knee injury?

    A: With a joint probability distribution.

    Larry Lesser

     

  • Q. How could you estimate the number of possible arrangements of bars (92.5% silver by weight) numbered 1 to 100?

    A. Sterling’s approximation!

    Larry Lesser

  • Teacher: To get the marginal of X from the joint pdf of X and Y, you should integrate.....
    Student: Can you go over why?
    Teacher: Correct!
     
    Larry Lesser and Dennis Pearl
  • Lyrics © Mary McLellan
    may sing to the tune of "Jingle Bell Rock"

    Central Limit Theorem is about the shape
    Of the sampling distribution and the population
    Central Limit Theorem is about the shape
    Of the sampling distribution and the population

    If n is large enough, it doesn’t matter
    The shape of the population,
    It (sampling distribution) will still be normal

    Central Limit Theorem is about the shape
    Of the sampling distribution
    And the parent, and the parent,
    Parent population…

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