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.
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!
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
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…