Monday, 24 April 2017

probability - $P(Y le X)=int_0^{infty} P(Y le X | X=x)f_X(x)dx$

I was looking at a solution of a probability exercise and the author of the solution uses the formula $$P(Y \le X)=\int_0^{\infty} P(Y \le X | X=x)f_X(x)dx$$ where $X$, $Y$ are the random variables $f_X$ is the density function of the random variable $X$. From where does this result come from?

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