# 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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