Timeline for conditional density wrt lebesgue measure

9 events

when toggle format	what		by	license	comment
Feb 12, 2015 at 19:02	comment	added	Zen		No: $\int_{\mathbb{R}} f_{X,Y}(x,y)d\lambda(y) = f_X(x)$, the marginal density of $X$.
Feb 12, 2015 at 18:43	comment	added	user2016445		oh sry my mistake :), $\int_{\mathbb{R}} f_{X,Y}(x,y)d\lambda(y) = 1$ it is true so everythin is fine. thank you it solved my problem.
Feb 12, 2015 at 18:19	comment	added	Zen		I wrote four equalities. Which one "doesn't hold"?
Feb 12, 2015 at 17:26	comment	added	user2016445		that is not true, this holds: $\int_A \mathbb{P}(X \in dx) \int_B f_{Y\|X}(x,y)\lambda(dy) = \int_{A \times B}f(x,y)\lambda^2(dx,dy)$
Feb 12, 2015 at 16:38	comment	added	Zen		$P(X\in A) = P(X\in A, Y\in\mathbb{R}) = \int_{A\times\mathbb{R}} f_{X,Y}(x,y)\,d\lambda^2(x,y) = \int_A\left(\int_\mathbb{R} f_{X,Y}(x,y)\,d\lambda(y)\right)d\lambda(x) = \int_A f_X(x)\,d\lambda(x)$
Feb 12, 2015 at 16:37	comment	added	Zen		Fubini: en.wikipedia.org/wiki/…
Feb 12, 2015 at 16:24	history	edited	user2016445	CC BY-SA 3.0	deleted 277 characters in body
Feb 12, 2015 at 15:59	history	edited	user2016445	CC BY-SA 3.0	added 6 characters in body
Feb 12, 2015 at 15:27	history	asked	user2016445	CC BY-SA 3.0