1
$\begingroup$

Let $x$ and $y$ be two independent random random variables with densities $f(x)$ and $f(y)$. I intend to define $\int \int_{-\infty}^x f(x)f(y)\,dy\,dx$ in relation to $E[x\mid x>y]$. I attempted the following. $E[x\mid x>y]=\frac{\int \int_{-\infty}^{x} xf(x)f(y)\,dy\,dx}{\int \int_{-\infty}^x f(x)f(y)\,dy\,dx}=\frac{\int xF_{y}(x)f(x)\,dx}{\int F_{y}(x)f(x)\,dx}$ where $F$ is CDF. I am not sure if this is correct, though. Can somebody please tell me if I am right or suggest me how to correct if I made a mistake.

  • 1
    Once you will have renamed $X$ and $Y$ (instead of $x$ and $y$) the i.i.d. random variables and $F$ (instead of $F_y$) the CDF, the formula shall be correct.2012-11-30

0 Answers 0