# Probability

may sing to the tune of "Take a Chance on Me" (ABBA)

If you roll your dice, and you want the price
calculate for me
probability
If you want to break even, gotta know the chance
(If you're not too careful then you can lose your pants.)
When you play a game, matching coins the name,
calculate for me
probability
If the chance for heads is p and for tails it's q
When we count the flipped coins up, we know what to do

Take a chance with me
(What's the distribution, honey?)
Take a chance with me

Look at geometric
Look at binomial
Get expected value
1 over p's the first one
np gives the second
sum up to find it's true
'Cos you know the Law!
Large Numbers says it's sure
Average X_i's to secure
the limit --
EX is where it goes (just as you would suppose)
Random stuff dies out
(infinity's got clout)

It sure can be tough, knowing when to bluff
calculate for me
probability
poker, bridge and backgammon's where you need the odds
& quantum mech will tell us that we're the dice of God
Markov models tell brokers when to sell
calculate for me
probability
DNA analysis and learning systems too
If you get some good priors, Bayes will work for you.

Take a chance with me
(Come on, conditional is cool)
Take a chance with me

Walk on the lattice
each edge is weighted equal
In dimension higher than two -
if you keep on goin' --
'Cos it's transient!
But some paths will recur
of this you can be sure
It's magic!
1 and 2D gets you there
as long as the walk is fair
though the variance strays, the paths don't get away
(straying paths don't quit, though there's no last visit)

If you roll your dice, and you want the price
calculate for me
probability
If you want to break even, gotta know the chance
(If you're not too careful then you can lose your pants.)
When you play a game, matching coins the name,
calculate for me
probability
If the chance for heads is p and for tails it's q
When we count the flipped coins up, we know what to do
(take a chance, take a chance, take a chance with me)

ba ba ba ba baa, ba ba ba ba baa
Calculate for me
Probability
poker, bridge, and backgammon, baby can't you see
it's the way the real world works - probability
(Take a chance, take a chance, take a chance with me)

ba ba ba ba baa, ba ba ba ba baa
it's reality--
probability