求指导本题解题过程，谢谢您！5、设二维随机变量(X,Y)在区域 = (x,y)|0leqslant xleqslant 2,0leqslant yleqslant 2 上服从均匀分而-|||-(1)随机变量X的数学期望E(X);(2)随机变量(X,Y)的协方差cov(X,Y).

步骤 1：确定联合概率密度函数
由于二维随机变量(X,Y)在区域 $G=\{ (x,y)|0\leqslant x\leqslant 2,0\leqslant y\leqslant 2\} $ 上服从均匀分布，因此联合概率密度函数为：
$$
f(x,y) = \begin{cases}
\dfrac{1}{4} & 0\leqslant x\leqslant 2, 0\leqslant y\leqslant 2 \\
0 & \text{其他}
\end{cases}
$$
步骤 2：计算边缘概率密度函数
边缘概率密度函数 $f_X(x)$ 和 $f_Y(y)$ 分别为：
$$
f_X(x) = \int_{0}^{2} f(x,y) dy = \int_{0}^{2} \dfrac{1}{4} dy = \dfrac{1}{2} \quad (0\leqslant x\leqslant 2)
$$
$$
f_Y(y) = \int_{0}^{2} f(x,y) dx = \int_{0}^{2} \dfrac{1}{4} dx = \dfrac{1}{2} \quad (0\leqslant y\leqslant 2)
$$
步骤 3：计算随机变量X的数学期望E(X)
$$
E(X) = \int_{0}^{2} x f_X(x) dx = \int_{0}^{2} x \cdot \dfrac{1}{2} dx = \dfrac{1}{2} \int_{0}^{2} x dx = \dfrac{1}{2} \cdot \dfrac{1}{2} x^2 \Big|_{0}^{2} = 1
$$
步骤 4：计算随机变量Y的数学期望E(Y)
$$
E(Y) = \int_{0}^{2} y f_Y(y) dy = \int_{0}^{2} y \cdot \dfrac{1}{2} dy = \dfrac{1}{2} \int_{0}^{2} y dy = \dfrac{1}{2} \cdot \dfrac{1}{2} y^2 \Big|_{0}^{2} = 1
$$
步骤 5：计算随机变量XY的数学期望E(XY)
$$
E(XY) = \int_{0}^{2} \int_{0}^{2} xy f(x,y) dx dy = \int_{0}^{2} \int_{0}^{2} xy \cdot \dfrac{1}{4} dx dy = \dfrac{1}{4} \int_{0}^{2} \int_{0}^{2} xy dx dy
$$
$$
= \dfrac{1}{4} \int_{0}^{2} y \left( \int_{0}^{2} x dx \right) dy = \dfrac{1}{4} \int_{0}^{2} y \cdot \dfrac{1}{2} x^2 \Big|_{0}^{2} dy = \dfrac{1}{4} \int_{0}^{2} y \cdot 2 dy = \dfrac{1}{2} \int_{0}^{2} y dy = \dfrac{1}{2} \cdot \dfrac{1}{2} y^2 \Big|_{0}^{2} = 1
$$
步骤 6：计算随机变量(X,Y)的协方差cov(X,Y)
$$
cov(X,Y) = E(XY) - E(X)E(Y) = 1 - 1 \cdot 1 = 0
$$