## Problem¶

\(P(Y<X)\) for any two independent random variables \(X,Y\)

## Solution¶

We just follow the definition:

\(P(Y<X) = \int_{-\infty}^{\infty}f_X(x)dx \int_{-\infty}^{x}f_Y(y)dy\)

\(P(Y <X) = \int F_X(y)f_X(x)dx\)

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