Math/Stat 443
Fall 2008
Homework 8 Due November 3 (Monday)
1. Exercise 4.81
2. Exercise 4.89
3. Exercise 4.98
Hint: Let Y=Z2. The mgf of Y is
MY
(
t
)
=E
(
eYt
)
=E
(
eZ2t
)
=∫
−∞
∞
ez2t1
√
2π
e
−z2
2dz
You can rewrite the integrand as a normal pdf. The simplified mgf
has a special form. Use the uniqueness property of mgfs to
identify the distribution of Y=Z2.
4. Exercise 4.124
5. Exercise 5.1 parts a b
6. Exercise 5.4
7. A random variable T has hazard rate r(t) = 1/(2-t) for 0<t<2.
Find the pdf f(t) and df F(t) of T.
