An example Let CO ( X .

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!

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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 )