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(Steps Shown) Let U_1 and U_2 be two independent Uniform (0,1) random variables, and V=min U_1, U_2 and W=max U_1, U_2. Find the joint CDF of V and W. Use part

Question: Let \(U_{1}\) and \(U_{2}\) be two independent Uniform \((0,1)\) random variables, and \(V=\min \left\{U_{1}, U_{2}\right\}\) and \(W=\max \left\{U_{1}, U_{2}\right\}\).

  1. Find the joint CDF of \(V\) and \(W\).
  2. Use part (a) to find the marginal PDF of \(W\).
  3. Find the conditional PDF of \(V\) given \(W=2 / 3\). Can you recognize the distribution?

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