corneel

08-27-2010, 10:38 PM

I jus dont seem to understand this concept "conditional e.v."

I do know the definitions: joint density f_X,Y , conditional density of X given Y=y, etc. (from textbook)

Also we have by definition

E( X|Y=y) = int_{R} x f_{X|Y} (x|y) dx ,

with f_{X|Y} (x|y) = f_X,Y (x,y) / f_Y (y) the conditional density of X given Y=y. This is no problem. (calculatting problems for me like E ( X | Y = 3) is not problemfor me..)

But, I have a lots of problems with for example the following :

Let X be a continuous r.v. ; calculatte E( X | a < X< b) .

how is this exactly defined... how to calculatte this, and why ?

I have two option for this kind :

first: E(X| a<X<b) = int_{R} E(X | a<X<b,X=t) f_X(t) dt = int_{a to b} t f_X(t) dt

is this wrong or not ? I do condition there i think.

second : E(X| a<X<b) = ( int_{a tob} t f_X(t) dt ) / P( a < X < b)

could please please someone give to me clear explanation out of definiton how to exactly calculatte this things rigorsly? thank a lot people !

I do know the definitions: joint density f_X,Y , conditional density of X given Y=y, etc. (from textbook)

Also we have by definition

E( X|Y=y) = int_{R} x f_{X|Y} (x|y) dx ,

with f_{X|Y} (x|y) = f_X,Y (x,y) / f_Y (y) the conditional density of X given Y=y. This is no problem. (calculatting problems for me like E ( X | Y = 3) is not problemfor me..)

But, I have a lots of problems with for example the following :

Let X be a continuous r.v. ; calculatte E( X | a < X< b) .

how is this exactly defined... how to calculatte this, and why ?

I have two option for this kind :

first: E(X| a<X<b) = int_{R} E(X | a<X<b,X=t) f_X(t) dt = int_{a to b} t f_X(t) dt

is this wrong or not ? I do condition there i think.

second : E(X| a<X<b) = ( int_{a tob} t f_X(t) dt ) / P( a < X < b)

could please please someone give to me clear explanation out of definiton how to exactly calculatte this things rigorsly? thank a lot people !