See G-10.3 for the marginal PDF of x1 .
41
11
11.1
Lecture 11 - October 7, 2004
Conditional Distributions and Expectations
Suppose we have 2 discrete random variables, X and Y . Then:
P r(X = x|Y = y ) = P (cfw_X = x|cfw_Y = y ) =
fx,y (x, y )
P (cfw_X =
So applying the formulas from above:
E [X ] = M 1 (t)|t=0 = .
2
x = M 2 (t)|t=0 [M 1 (t)]2 |t=0 = 2 + 2 2 = 2 .
31
9
Lecture 9 - September 30, 2004
Note that we can rewrite the characterist polynomial formula from last time as:
(X ) = E [eitX ] = E [cos(
6.3
Mathematical Expectation
Denition 1a: Let (, A, P ) be a probability space and let X : be a scalar
RV with a distribution Px and let u : be a (B, B)-measurable function.
Suppose X is a discrete RV with PDF, fx (x), then the expected value (mathemati
See notes for Lebesgue-Borel Measure. Note the lebesgue integral will not in general
equal the Reimann integral in all cases.
4.2
Random Variables
Consider again the 2-coin ip example.
= cfw_T T, T H, HT, HH .
+ = cfw_0, 1, 2.
X : + .
Denote:
0 if = T
Economics 623: Econometrics
Matthew Chesnes
Updated: January 1, 2005
These are Matthew Chesnes notes from a course taught by Ingmar Prucha.
1
Lecture 1: August 31, 2004
1.1
Motivation for the Course
Consider a simple example of a linear consumption funct