Thread: Random Variables, Density, and Derivatives

A point Q is chosen at random inside the unit square. What is the density function of the sum of the coordinates of the point Q? What is the density function of the product of the coordinates of the point Q? Use geometry to find these densities.

I know that derivatives must be involved.

Originally Posted by diddledabble

A point Q is chosen at random inside the unit square. What is the density function of the sum of the coordinates of the point Q? What is the density function of the product of the coordinates of the point Q? Use geometry to find these densities.

I know that derivatives must be involved.

X ~ U(0, 1) and Y ~ U(0, 1) and X and Y are independent. Your job is to find the distribution of V = X + Y and W = XY.