Chapter 4.2, Problem 12E

The cdf for X (= measurement error) of Exercise 3 is

     $F(x)=\{\begin{array}{ll}0\hfill & x<-2\hfill \\ \frac{1}{2}+\frac{3}{32}\left(4x-\frac{x^3}{3}\right)\hfill & -2<x<2\hfill \\ 1\hfill & 2\le x\hfill \end{array}$

a. Compute P(X < 0).

b. Compute P(−1 < X < 1).

c. Compute P(.5 < X).

d. Verify that f (x) is as given in Exercise 3 by obtaining F′(x).

e. Verify that $\tilde{\mu }=0$.