I have two independent Rayleigh distributed random variable: $X_1$ and $X_2$. I would like to derive the probability of $P(X_1 < X_2| X_1 > \gamma)$.
I started the derivation as: $P(X_1 < X_2| X_1 > \gamma) = \frac{\int_\gamma^\infty \left[ \int^{\infty}_{x_1} f_{x_1,x_2} dx_2 \right] dx_1}{P(X_1 > \gamma)}$
Then, $\frac{\int_\gamma^\infty \left[ \int^{\infty}_{x_1} f_{x_1,x_2} dx_2 \right] dx_1}{1 - \int_{-\infty}^\gamma f_{x_1}dx_1}$.
Am I doing it correctly? Thank you.