A calculus problem about statistics

The random variable \((X, Y)\) has a density function: \[f(x,y) = \begin{cases} kye^{-x} & \text {if } 0 < x < y < 2x \\ 0 & \text {for all other points} \end{cases}\]

Find \(k\)

Submit \(\lfloor 2000k \rfloor\).

Notation: \(\lfloor \cdot \rfloor\) denotes the floor function .

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