density function?

Question

3. 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
0 otherwise

What is the density function of X and Y?

Answer 1

The "density" function of X and Y just represents a way to calculate the damages related to a farm insurance. The use of the word Density is not literally like the density of a liquid, solid or gas, where density is mass/volume. However, in a contextual sense the apportioning of total damage as a combination of damage to the house AND damage to rest of the property is like giving weight of mass of a portion to the whole.

Thus, the density function is just an equation to solve the total damage by assigning the letter X for the damage of the house itself and the letter Y to the damage to the rest of the property.

Since there are 2 variables, then so say that the density function is a function of X and Y. This is symbolically represented by f(x,y) or f (X,Y). Had there been another variable Z, then you say a density function of X, Y and Z or f (x,y,z).

Also the equation is giving you additional info about the values of x and y. Think about it x>0 because a positive value means there was damage to the house. It does not make sense for a negative value for damage, when that means essentially, there is no damage, contrary to what you are actually measuring, --DAMAGE.

Or put another way, you may just call it a density equation for calculating damages.

Answer 2

Do you own home work.

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