Suppose that, as in Exercise 5.11, Y1 and Y2 are uniformly distributed over the triangle shaded in the accompanying diagram. Find E(Y1Y2).

Reference

Suppose that Y1 and Y2 are uniformly distributed over the triangle shaded in the accompanying diagram.

a Find P(Y1 ≤ 3/4, Y2 ≤ 3/4).

b Find P(Y1 − Y2 ≥ 0).

Solution:

Step 1 of 2:

To find for the given diagram.

From the above diagram, we know that the equation of line joining (-1,0) and (0,1) is y = x +1.

And the equation of the line joining (0,1) and (1,0) is y = 1- x.

Then,