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Probability

  • 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…

  • Lyrics © Mary McLellan
    may sing to the tune of "All I Wanna Do" by Sheryl Crow

    Probability of at least one
    Listing all the combinations is not fun

    Probability of at least one
    Listing all the combinations is not fun

    Probability of at least one
    Easier with…
    One minus the probability of none

    Repeat

  • Lyrics © Mary McLellan
    may sing to the tune of "Bare Necessities"

    If you do many trials
    Many, many trials
    The cumulative probability
    It will settle down to the true probability
    The law of large numbers you see

    Repeat

  • Lyrics © Mary McLellan
    may sing to the tune of "Oh My Darlin', Clementine"

    Independent, independent, independent
    When the fact that you are one thing
    Does not change the rate

    Independent, independent, independent
    When the fact that you are one thing
    Does not change the rate

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