Question

Find the probability that the sum of random variables X and Y is greater than 4, expressed as a fraction. The joint probability density function of X and Y is given by:

f(x, y) = {
k(x + y), 0 < x < 2, 1 < y < 4
0, otherwise

Answer 1

To find the probability that the sum of random variables X and Y is greater than 4, we need to integrate the joint probability density function over the appropriate region.

Step-by-step explanation:

To find the probability that the sum of random variables X and Y is greater than 4, we need to integrate the joint probability density function over the appropriate region. The joint probability density function is given by:

f(x, y) = { k(x + y), 0 < x < 2, 1 < y < 4
0, otherwise

To find the value of k, we need to set up and solve the double integral:

k = ∫∫ f(x, y) dx dy

Once we have the value of k, we can then set up and solve the double integral to find the probability:

P(X + Y > 4) = ∫∫ f(x, y) dx dy