Let X and Y be jointly continuous random variables with joint PDF fX,Y(x,y) = 6e^-(2x+3y) for x,y >= 0. Find fX(x) and f_Y(y).

1. Let $X$ and $Y$ be jointly continuous random variables with joint PDF

$$f_{X,Y}(x,y) = \begin{cases} 6e^{-(2x+3y)}, & x,y \ge 0 \\ 0, & \text{otherwise} \end{cases}$$

a) Find $f_X(x)$ and $f_Y(y)$.

Step 1: Find the marginal PDF $f_X(x)$ by integrating $f_{X,Y}(x,y)$ with respect to $y$.

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