**COMING ATTRACTIONS FOR EECS 501**

**For Problem Set #4:**
- #2: Transformation: z=x+y; w=x-y.
- #3: Assume x,y are independent rvs.

**For Problem Set #3:**
- #4: Joint pdf f
_{a,b,c}(A,B,C)=
f_{a}(A)f_{b}(B)f_{c}(C)=
f_{x}(A)f_{x}(B)f_{x}(C)

since a,b,c are independent and identically distributed.

- #6: What's confusing is f
_{x}(X) is a *function*
as well as a desired pdf.

Also, x_{i} and y_{i} are independent and
*uniformly distributed* in [0,1).

**For countable vs. uncountable sets:**
- Provide a 1-1 correspondence with a set of known cardinality:

- {integers}, {rationals}, {lattice points} are all countable;
- interval [0,1), {reals}, (power set of countably infinite set) are all uncountable.

**For conditional probability:**
- Pr[A|B]=Pr[AB]/Pr[B]=Pr[AB]/(Pr[AB]+Pr[A'B]);
- Note the form C/(C+D) in this formula;
- Remember to divide by Pr[GIVEN event].

**The Cantor set (covered in recitation):**
- Significance to EECS 501: The Cantor set is uncountable,
- since its endpoints are not rational numbers.
- Yet Pr[Cantor set]=0 for the wheel of fortune experiment!
- Why are the endpoints irrational? Suppose they were rational.
- Then their decimal expansions would be "eventually zero" for some finite N.
- But the construction of the Cantor set makes it clear this is not the case.