The continuous distribution with a density f(x) is said to be symmetric if for a number s called a center of symmetry, and for any x > 0,

(a) Which distributions considered in Sections 1.1 and 2 are symmetric? With respect to which centers of symmetry?

(b) Give an example showing that the center of symmetry does not have to coincide with one of the values of the r.v.

(c) Show that the above definition of symmetric distribution is equivalent to the requirement P(X > s+x) = P(X 0.