If two random variables have the joint probability density function

\(f(x, y) = \left\{\begin{matrix}k(2x + 3y), \enspace for \enspace 0 \leq x \leq 1, \enspace 0 \leq y \leq 1 \\ 0, otherwise\end{matrix}\right.\)

Find (i) constant k (ii) conditional probability density function of X (iii) Identify whether X and Y are independent.

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