I’ve just started studying bivariate distributions, precisely “Conditional density of X2 conditionally on X1 = x1”.
First of all, the slides of this topic give me the following formulas that I need to use for the next example which I didn’t understand how to solve it.
The formulas are:
Second, this is the example. “c” is a constant.
From this, I didn’t understand how the professor get fX (x), fY (y) and the conditional expectation and variance.
Is there anyone who can help me? An explanation would be appreciated.
Thanks in advancd!
- Attachment 1
- Attachment 2
An exampleLet CO( X . V ( X , y ) = 1if O < < < 1 and x – c s y S x tootherwiseAfter some computation1 ) ( x ( X ) = 11 0 < < 1O otherwise2 ) FX( ) = 120min ( 1 , y + c ) – max ( O y – c ) – csy ST tootherwiseSuppose you know that X = xfrix = X ( V ) =if X – c S y S x tootherwise3 ) E ( V X = x ) = x4 ) V ( V X = x )