From the “north pole” N of a circle with diameter 1, a point Q on the circle is mapped to a point t on the line by its projection from N, as illustrated in Figure 8.2. a. What part of the circle is...

From the “north pole” N of a circle with diameter 1, a point Q on the circle is mapped to a point t on the line by its projection from N, as illustrated in Figure 8.2.

a. What part of the circle is mapped to the interval [1, ∞)?

b. Compute the distribution function of Z using the correspondence between t and ϕ.

c. Compute the probability density function of Z.