- Homework is from the textbook (9th edition) – required
- Homework is assigned every Friday on ELMS
- Due during discussion on the next Thursday
- No curve on any grades
Midterm Exams:
- Week of Feb. 24th (Week 5)
- Week of April 6th (Week 11)
This course is about probability theory (2/3rds) and statistics (1/3rd):
- Sample space and events
- Discrete random variables
- Continuous random variables
- Joint distributions and random samples
- Advanced topics in probability
- Point estimators and confidence intervals
These topics correspond to Chapters 2 through 7 in the textbook.
Probability theory is the study of randomness and uncertainty quantitatively.
Ex. What’s the probability that…
- …you toss a coin and it lands on Heads?
- …you roll a die and it lands on an odd number?
- …the S&P 500 index will be above 3400 tomorrow?
- …the highest temperature today is higher than the day after tomorrow?
Each of these is referred to as an event.
We assign a value to an event, called the probability of the event.
We can represent events by the set of all outcomes that fulfill that event.
Ex.
- {Heads}
- {odd numbers} or {1,3,5}
- {I>3400}
- {T1>T2}
(Note that there are infinitely many outcomes that satisfy the 3rd and 4th events above, but only finitely many outcomes that satisfy the 1st and 2nd.)
Definition. The collection of all possible outcomes for an experiment is called the sample space S of the experiment.
Ex.
- S={Heads,Tails}
- S={1,2,3,4,5,6}
- S=(0,∞)
- S=(a,∞)×(a,∞) (Cartesian product)
With this definition, events are simply subsets of the sample space of the experiment they arise form.
An event is called simple if it contains one outcome. (ex. {Heads})
Likewise, an event is called compound if it contains more than one outcome. (ex. {1,3,5})
The probability of an event A is then denoted as P(A). (ex. P({Heads})=21)