Hi, all. I happened to think about a problem about conditional PDF:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]x_2=x_1+a, x_1 \approx \mathcal{N}(0,1), a \approx \mathcal{N}(0,1)[/itex]

so the conditional PDF of [itex]f(x_2|x_1), f(x_1|x_2)[/itex] would both be

[itex]f(x_2|x_1)=f(x_1|x_2)=\frac{1}{\sqrt{2\pi}}\exp{(-\frac{(x_1-x_2)^2}{2})}[/itex]

And it is clear that [itex]f(x_1)[/itex] and [itex]f(x_2)[/itex] are not identical, so

[itex]f(x_1)f(x_2|x_1) \neq f(x_2)f(x_1|x_2)[/itex]

How does this occur?

Thanks in advance.

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# Question on Conditional PDF

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