Question: If Z is a real-valued random variable with density bounded by C, then show that, for any random variable W, dK (W, Z)

If Z is a real-valued random variable with density bounded by C, then show that, for any random variable W, dK (W, Z) ≤ 

2CdW (W, Z) , where dK is the Kolmogorov–Smirnov (or sup or uniform) metric between distribution functions, and dW is the Wasserstein metric.

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