Math Solutions

[Solved] Suppose the joint PDF of X and Y is f_X, Y(x,

Question: Suppose the joint PDF of \(X\) and \(Y\) is

\[f_{X, Y}(x, y)=\left\{\begin{array}{l} 3 y \text { if } 0 \leq x \leq y \leq 1 \\ 0 \text { otherwise } \end{array}\right.\]

Let \(Z=Y-X\).

  1. Find \(E(Z \mid Z \leq 1 / 2)\).
  2. Find \(P(Y<\sqrt{X})\).
  3. Find marginal PDF of \(X\) and \(Y\). Are these random variables independent? Give reason for your answer.

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Deliverable: Word Document


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