[Solution Library] The joint probability density function of X and Y, is given by p(x, y)=2(x+y) I0 ≤q x ≤q y ≤q 1 Let Z=E(X \mid Y). Compute the first

Question: The joint probability density function of $X$ and $Y$, is given by

\[p(x, y)=2(x+y) I\{0 \leq x \leq y \leq 1\}\]

Let $Z=E(X \mid Y)$. Compute the first and second moments of $Z$.
Let $W=2 X-Y$. Find the distribution function of $W$.
Let $\theta =E{{W}^{2}}$ and $\left\{X_{i}, Y_{i}\right\}_{i=1}^{n}$ be a random sample from $p(x, y)$. State the sample analogue estimator and its expected value.

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[Solution Library] The joint probability density function of X and Y, is given by p(x, y)=2(x+y) I0 ≤q x ≤q y ≤q 1 Let Z=E(X \mid Y). Compute the first

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