# Probability

• ### Coveyou on Random Numbers

The generation of random numbers is too important to be left to chance.

Robert R. Coveyou (1915 - 1996)

• ### Peirce on Probability

The theory of probabilities is simply the science of logic quantitatively treated.

Charles Saunders Peirce (1839 - 1914)

• ### Kaplan on Statistical Models

The words "model" and "mode" have, indeed, the same root; today, model building is science a la mode.

Abraham Kaplan (1918 - 1993)

• ### Poincare on Chance

Chance is only the measure of our ignorance.

Jules Henri Poincare (1854 - 1912)

• ### Birthday Song

may sing to tune of "Happy Birthday to You" (Mildred J Hill and Patty Smith Hill)

Happy birthday to you--
Bring another 22:
Then we'll have even chances
Of a match in this room...
Or many more!

Happy birthday to me--
Bring another two-fifty-three:
Then I'll have even chances
Someone matches with ME...
Or many more!

• ### Probability Man

may sing to tune of "Mr. Tambourine Man" (Bob Dylan)

Hey Probability Man, flip a coin for me,
I don't study and I never really learned how to.
Hey Probability Man, roll those dice for me,
As you're walking to your classroom I'll come following you.

Help me take the steps to compute a cdf,
Calculate a pmf, to derive an mgf,
and take limits from the left, just learning terms
won't help my understanding.
How hard can it be to integrate a density,
or to calculate a mean, or infer what is not seen,
I promise to learn Calculus.

Hey Probability Man, pick a card for me,
I don't study and I never really learned how to.
Hey Probability Man, spin that wheel for me,
As you're walking to your classroom I'll come following you.

My memory is gone when the process is Poisson,
Or even Gaussian; my transforming is undone
With the wrong Jacobian, my mind's made up,
I need to understand you.
Teach me all you know, teach me now I cannot wait
to learn how to correlate, or when one should integrate,
I want to learn everthing.

Hey Probability Man, flip a coin for me,
I don't study and I never really learned how to.
Hey Probability Man, roll those dice for me,
As you're walking to your classroom I'll come following you.

• ### Bayesians in the Night

Lyrics copyright by Bent Natvig and Morris DeGroot
May sing to the tune of "Strangers in the Night" (Kaenpfert, Singleton, and Snyder)

Bayesians in the night
With exchangeable glances
Assessing in the night
The prior chances
We'd be sharing risk
Before the night was through.

Was so inviting
Was so exciting
Something in my model
Told me I must have you.

Bayesians in the night
Two statisticians
We were Bayesians in the night
Then came the moment when we
walked down to the sea
Under a fault tree
Our likelihoods were close together
And Sir Ronald lost his final feather

Ever since that night
To have coherence
It turned out all right
For Bayesians in the night.

• ### Means Will Follow You

Lyrics copyright by Dennis Pearl and Peter Sprangers
may sing to the tune of "I Will Follow You" (Ricky Nelson)

Follow you as de Moivre would show
There isn't a skewness too steep
An "n" so high it can't keep it away

And since the central limit shows
That near you I always must be
And nothing can keep you from me
You are my density

If n big, if n big, if n big
Then Normal you will follow, will follow, will follow
You'll always be symmetric, symmetric, symmetric
With smaller deviation, deviation, deviation

Follow you as de Moivre would show
There isn't a skewness too steep
An "n" so high it can't keep it away
Keep it away, away from your curve

If n big, if n big, if n big
Then Normal you will follow, will follow, will follow
You'll always be symmetric, symmetric, symmetric
With smaller deviation, deviation, deviation

Follow you as de Moivre would show
There isn't a skewness too steep
An "n" so high it can't keep it away
Keep it away, away from your curve

And Normal then will follow

• ### Sigma Fields

may sing to tune of "Strawberry Fields" (John Lennon, Paul McCartney)

Let me take you down, 'cause I'm going to the sigma-fields
Lebesgue things are real, and nothing to get hung about
Sigma Fields forever

Living is easy with sets closed, and understanding all you see
Probabilities map to zero-one and it all works out, that's what matters most to me
Let me take you down, 'cause I'm going to the sigma-fields
When things are Borel, there's nothing to get hung about
Sigma Fields forever

Sets of sets are events, I mean it must be probability
That is you know it can't go negative or over one, that is I think it's not too bad
Let me take you down, 'cause I'm going to the sigma-fields
When things are Borel, there's nothing to get hung about
Sigma Fields forever

Always, no sometimes, probability, but you know I know a gambler's scheme
I think I know the mean, but the measure is all wrong, that is I think I disagree
Let me take you down, 'cause I'm going to the sigma-fields
Lebesgue things are real, and nothing to get hung about
Sigma Fields forever
Sigma Fields forever
Sigma Fields forever

• ### Prior

Lyric by Mark Glickman
may sing to the tune of "Venus" (The Shocking Blue)

don't know where it should go.
A method to express this knowledge
is what I don't know!

I've got it, yeah, baby, I've got it!
Well, I'm the thesis, I'm the prior that you require!
Well, I'm the thesis, I'm the prior that you require!

I had myself a complex model
I didn't know how to constrain.
I tried to estimate the unknowns.
My attempts were in vain!

I've got it, yeah, baby, I've got it!
Well, I'm the thesis, I'm the prior that you require!
Well, I'm the thesis, I'm the prior that you require!