MATH240 HOMEWORK IV
(Due: next class time for each section)
1. The density function of X is
otherwise
xbxa
xf x
0
102
(1)
If E[X] = 3/5, find a and b. What is Var[X]?
2. Given the joint PMF of X and Y as
(a) Find E[X], E[Y], and E[XY],
(b) Show that X and Y are uncorrelated,
(c) Determine if X and Y are independent or not.
3. The joint density function of X and Y is
otherwise
yx
yx
yxf yx
0
10,10
,,
(2)
a) Are X and Y independent?
b) Find the probability density function of X?
c) Find P(X+Y < 1)=?
4. Two fair dice are rolled. Find the joint probability mass function of X and
Y when X is the largest value obtained on any die and Y is the sum of the
values.
5. Suppose the joint density function of X and Y is given by
otherwise
yx
y
ee
yxf
yyx
yx
0
0,0
,
/
, (3)
a) Find the conditional probability density of X, given that Y=y.
b) Find P(X > 1 | Y = y).
