Bayesian networks
Each family has children until it has a boy, and then stops.
Each family has children until it has a boy, and then stops. What is the expected fraction of girls in the population?
If you flip a coin and it comes up heads 10 times, what is the probability you have the fair coin?
Simpson's Paradox
ELISA AIDS test.
ELISA AIDS test. What is the probability you have the disease given a positive test result?
The probablistic graphical model
The probablistic graphical model
Y -> Q | v X -> Z -> W
RISK
Observed probabilities of getting cancer broken out by whether you smoke and whether you have tar in your lungs
You roll a 6-sided die and keep a running sum.
You roll a 6-sided die and keep a running sum. What is the probability the sum reaches exactly 30?
How many times do you need to flip a fair coin to get n heads in a row?
If you flip a coin repeatedly, which is more likely to occur first, HTH or HTT?
Mr.
Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?
Monty Hall problem
Pascal's triangle
A single bank teller can service a customer in 10 minutes.
A single bank teller can service a customer in 10 minutes. If one customer comes in every 11 minutes on average, what is the expected length of the line?
Random walk: starting at 0 and moving left or right with equal probability, how many steps do you expect to take before reaching 10?
Mr.
Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
Teasing apart correlation and causality.
Teasing apart correlation and causality. From http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/
First, observe the joint probability distribution of:
Encode this as a graphical model.
This encodes the probability distribution of smoking and cancer.
This encodes the probability distribution of smoking and cancer. We can use it to calculate p(cancer) and p(cancer|smoking).
95% of smokers have tar in their lungs 5% of nonsmokers have tar in their lungs
Mr.
Mr. Miller has two children. One of them is a boy born on Tuesday. What is the probability both children are boys?
Given a biased coin with unknown bias distributed according to prior
,
after flipping nflips
times and observing successes
heads,
what is the posterior distribution of the bias?
Given a Markov model for the weather, if it is rainy on thursday, what was the likely weather on monday?