Sums of normal in the positive quadrant let x and y be two

Question

Question: Sums of normal in the positive quadrant. Let X and Y be two independent standard normal variables:

a) Calculate P(X > 0, Y > 0, X + Y 1).

b) Find the conditional density of X + Y given X > and Y > 0, and sketch its graph.

c) Find, approximately, the median and the mode of this distribution.