1. ## Maths help?! question about joint density functions and insurance

A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is

f (x,y) = 6 [1 - (x + y)] for x > 0, y > 0, x + y < 1
and 0 elsewhere

how do you determine the probability that the portion of a claim representing damage to the house is less than 0.2 ? thank you for your time

2. Originally Posted by Statsnoob2718
A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is

f (x,y) = 6 [1 - (x + y)] for x > 0, y > 0, x + y < 1
and 0 elsewhere

how do you determine the probability that the portion of a claim representing damage to the house is less than 0.2 ? thank you for your time
Draw the region defined by the support. Then it should be clear to you that $\displaystyle \Pr(X < 0.2) = \int_{x = 0}^{x = 0.2} \int_{y = 0}^{y = 1-x} f(x, y) \, dy \, dx$.