1. Introduction to Probability and Statistics
4th Week (3/29)
1. Bayer’s Theorem
2. Random Variables
3. Probability Distributions
4. Mathematical Expectations (intro)
2. What would you do…..
IF a medical test (tumor marker) inform you that you
got an incurable disease (i.e. Pancreases Cancer)
1.Cry
2.Use your remaining time for some important thing
3.Invent a new iphone
5. Baye’s Theorem: When do we need?
• Why do we care??
• Why is Bayes’ Rule useful??
• It turns out that sometimes it is very useful to be able to
“flip” conditional probabilities. That is, we may know the
probability of A given B, but the probability of B given A
may not be obvious.
8. Las Vegas
777(Jack Pot) => 1 million dollars (1)
Others: Bam => 0 dollars (0)
How often do you get “1”?
How much do you put money to get
1 million dollars?
21. Discrete Joint Distribution Function
Probability Function (it’s like a point)
Understand the difference between
Distribution Function (it’s like an area)
23. Marginal Distribution Function
We call them the marginal distribution functions, or simply the distribution
functions, of X and Y, respectively.
Density Function