0 votes 0 votes Let \(X\) and \(Y\) have a joint probability density function given by \[ f_{X,Y}(x, y) = \begin{cases} 2 & \text{if } 0 \leq x \leq 1 - y \text{ and } 0 \leq y \leq 1 \\ 0 & \text{otherwise} \end{cases} \] If \(f_Y\) denotes the marginal probability density function of \(Y\), then \(f_Y(1/2)\) is given by Probability probability + – rajveer43 asked Jan 11 rajveer43 107 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes If \( f_Y \) denotes the marginal probability density function of \( Y \), then \( f_Y(1/2) \) is given by \[ f_Y(1/2) = \int_{-\infty}^{\infty} f_{X,Y}(x, 1/2) \, dx \] \[ = \int_{0}^{1/2} 2 \, dx \] \[ = [2x]_{0}^{1/2} \] \[ = 1 \] rajveer43 answered Jan 11 rajveer43 comment Share Follow See all 0 reply Please log in or register to add a comment.