# Probability

• ### 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

• ### Silver Arrangements

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

• ### A marginal joke

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
• ### Central Limit Theorem

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…

• ### Probability of At Least One

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

• ### Law of Large Numbers

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

• ### Independent

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