# Probability Density Function

1. Apr 27, 2010

### Fuquan22

1. The problem statement, all variables and given/known data
A point Q is chosen at random inside the unit square. What is the density function of the sum of the coordinates of point Q? What is the density function of the product of the coordinates of the point Q? Use geometry to find these densities.

2. Relevant equations
P(a < X < b) = Integral (a,b) of f(x)dx

3. The attempt at a solution
I know that the interval for the first part has to be between 0 and 2, but I don't know f(x)

2. Apr 27, 2010

### lanedance

choosing a point at random from unit square is in effect equivalent to choosing 2 independent uniform random variables, say X & Y, on the interval [0,1].

Then you want to find the density function for Z = X + Y

Last edited: Apr 27, 2010
3. Apr 27, 2010

### Fuquan22

Yes but how do i go about finding that density function? I just don't know the final step to calculating a density function.

4. Apr 27, 2010

### zachzach

It says use geometry. So does drawing lines of constant x+y help you solve it?

5. Apr 27, 2010