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ECE 302 Fall 2009 Division 2
Homework 6, due in class 10/15/2009
Problem 1.
Let
X
and
Y
be independent random variables. Random variable
X
has a discrete
uniform distribution over the set
{
1
,
2
,
3
}
, and
Y
has a discrete uniform distribution over the set
{
1
,
3
}
. Let
V
=
X
+
Y
, and
W
=
X

Y
.
(a)
Are
V
and
W
independent? Explain without calculations.
(b)
Find and plot
p
V
(
v
). Also, determine
E
[
V
] and var(
V
).
(c)
Find and show in a diagram
p
V,W
(
v,w
).
(d)
Find
E
[
V

W >
0].
(e)
Find the conditional variance of
W
given the event
V
= 4.
(f)
Find and plot the conditional PMF
p
X

V
(
x

v
), for all values.
Problem 2.
An insurance company writes a policy to the e±ect that an amount of money
x
must be
paid if some event
A
occurs within a year. If the company estimates that
A
will occur within a year
with probability
p
, what should it charge the customer so that its expected pro²t will be 10% of
x
?
Problem 3
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 Spring '08
 Donnely

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