Please only answer part d. I have asked parts a-c in a separate post **Joint Density Function of Random Variables X and Y**Consider the random variables with X and Y with joint density function given by:\[f(x,y) = \begin{cases} k(y + x) & \text{when } x, y \in [0, 2] \\0 & \text{else}\end{cases}\]**Tasks:**a. **Draw a Picture of the Domain**: Illustrate the region where \( f(x,y) \neq 0 \).b. **Solve for k**: Determine the value of \( k \) so that \( f(x,y) \) is a valid density function.c. **Probability of X < 1**: Calculate the probability that the random variable X is less than 1.d. **Probability of X > Y**: Compute \( P(X > Y) \).**Explanation:**- **Domain Picture**: The domain is the square region on the xy-plane where both x and y range from 0 to 2.- **Finding k**: Integrate \( f(x,y) \) over the specified domain to ensure the total probability equals 1.- **Calculating Probabilities**: - For \( X < 1 \): Adjust the bounds of integration accordingly. - For \( X > Y \): Evaluate the area under the curve where X is greater than Y within the specified region.

Name: Please only answer part d. I have asked parts a-c in a separate post *
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Please only answer part d. I have asked parts a-c in a separate post **Joint Density Function of Random Variables X and Y**Consider the random variables with X and Y with joint density function given by:\[f(x,y) = \begin{cases} k(y + x) & \text{when