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Suppose that I observe $z_i=Min[\frac{n-1}{n}v_i,w_i]$ where $v_i\sim U[0,\bar{v}]$ and $w_i\sim U[0,\lambda \bar{v}]$. For all intents and purposes in what I am doing I assume: $\bar{v}>0, \lambda>1,n>=2$.

How could I derive the PDF and CDF of $z_i$ ?

I know how to accomplish this with order statistic when there is no transformation inside the min function, but am getting lost when I have to transform one of the random variables by a function.

Many thanks!

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