Q4 Comprehension 2 Marks 22 Dec 2024
Passage
Based on the above data, answer the given subquestions. The joint density of two continuous random variables X X X and Y Y Y is given as f X Y ( x , y ) = { c e − ( x + 2 y ) , 0 ≤ x < ∞ , 0 ≤ y < ∞ 0 , otherwise f_{XY}(x, y) = \begin{cases} c e^{-(x+2y)}, & 0 \le x < \infty, 0 \le y < \infty \\ 0, & \text{otherwise} \end{cases} f X Y ( x , y ) = { c e − ( x + 2 y ) , 0 , 0 ≤ x < ∞ , 0 ≤ y < ∞ otherwise where c c c is a constant.
Find the Marginal distribution of X X X . A f X ( x ) = { 2 e − x , 0 < x < ∞ 0 , otherwise f_X(x) = \begin{cases} 2e^{-x}, & 0 < x < \infty \\ 0, & \text{otherwise} \end{cases} f X ( x ) = { 2 e − x , 0 , 0 < x < ∞ otherwise B f X ( x ) = { e − x , 0 ≤ x < ∞ 0 , otherwise f_X(x) = \begin{cases} e^{-x}, & 0 \le x < \infty \\ 0, & \text{otherwise} \end{cases} f X ( x ) = { e − x , 0 , 0 ≤ x < ∞ otherwise C f X ( x ) = { e − 2 x , 0 ≤ y < ∞ 0 , otherwise f_X(x) = \begin{cases} e^{-2x}, & 0 \le y < \infty \\ 0, & \text{otherwise} \end{cases} f X ( x ) = { e − 2 x , 0 , 0 ≤ y < ∞ otherwise D f X ( x ) = { 2 e − 2 x , 0 ≤ x < ∞ 0 , otherwise f_X(x) = \begin{cases} 2e^{-2x}, & 0 \le x < \infty \\ 0, & \text{otherwise} \end{cases} f X ( x ) = { 2 e − 2 x , 0 , 0 ≤ x < ∞ otherwise 