Question: \(X\) and \(Y\) have joint density function \(f_{x x}(x, y)=\left\{\begin{array}{l}B x y, 0 \leq x \leq y \leq 1, \\ 0, \text { otherwise. }\end{array}\right.\)

1. Find \(B\).
2. Find and sketch the marginal density functions \(f_{x}(x)\) and \(f_{r}(y)\).
3. Prove or disprove that \(X\), \(Y\) are independent.
4. Find \(E\{X\}, E\{Y\}\) and \(E\{X Y\}\).
5. Prove or disprove that \(X\), \(Y\) are uncorrelated.
6. Find and sketch the conditional density functions \(f(y \mid x)\) and \(f(y \mid x)\).
7. Find \(E\{Y \mid x\}, E\{Y \mid X\}\) and \(E\{X \mid y\}, E\{X \mid Y\}\)

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