**Problem Statement:**Let $ X $ and $ Y $ be continuous random variables with the joint density function:\[f_{XY}(x, y) = \begin{cases} \frac{8}{3}xy & \text{for } 0 \leq x \leq 1, \, x \leq y \leq 2x \\0 & \text{otherwise.}\end{cases}\]**Task:**Find the covariance $ \text{Cov}(X, Y) $.**Explanation:**The problem involves finding the covariance between two continuous random variables $ X $ and $ Y $ given their joint probability density function. The joint density function is defined in a piecewise manner, with a specific range for $ x $ and $ y $ where the function is non-zero, and zero elsewhere.

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Let X and Y be continuous random variables with joint density function Sxy(x,y) = {ry 0

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Question

**Problem Statement:**

Let $ X $ and $ Y $ be continuous random variables with the joint density function:

\[
f_{XY}(x, y) =
\begin{cases}
\frac{8}{3}xy & \text{for } 0 \leq x \leq 1, \, x \leq y \leq 2x \\
0 & \text{otherwise.}
\end{cases}
\]

**Task:**

Find the covariance $ \text{Cov}(X, Y) $.

**Explanation:**

The problem involves finding the covariance between two continuous random variables $ X $ and $ Y $ given their joint probability density function. The joint density function is defined in a piecewise manner, with a specific range for $ x $ and $ y $ where the function is non-zero, and zero elsewhere.

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