Consider the following joint distribution of random variables $\mathrm{X}$ and $\mathrm{Y}$:
$f(x, y)=\left\{\begin{array}{cl}\frac{x\left(1+3 y^2\right)}{4}, & 0 \leq x \leq 2,0 \leq y \leq 1 \\ 0, & \text { otherwise }\end{array}\right.$
Which one or more of the following statements is/are correct?
- $\mathrm{X}$ and $\mathrm{Y}$ are mutually uncorrelated.
- $\mathrm{X}$ and $\mathrm{Y}$ are mutually independent.
- The mean of $\mathrm{X}$ is $1$.
- The mean of $\mathrm{Y}$ is $0.5$.
