Iarbus told Queen Dido that she could have as much land as could be encircled with a bulls hide for the founding of Carthage. Queen Dido had a large bulls hide cut into extremely thin strips to make a long cord, which she used to encircle a large area. Assume that the cord is used to form a semi-circle along a straight coastline. Also assume that the length of the cord L is exponentially distributed with parameter . Compute the following.

(a) What is the complementary distribution function of the area A of the new city?

(b) What is the c.d.f. of A?