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# Probability

• ### The Effect of Coffee

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

Sara Venkatraman

• ### Another Light Bulb Joke

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

Answer: That depends on the model

Robert Weiss

• ### Divvy up the Stakes

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.

• ### Empirical Rule

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

(Repeat Chorus)

• ### Central Limit Theorem

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]
• ### The Knee

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