STOR 435
Handout 7
Sections 4.44.6
Example 1
(Example 4a; Functions of a random variable)
.
X
is a random
variable with
P
(
X
=

1) =
.
2,
P
(
X
= 0) =
.
5 and
P
(
X
= 1) =
.
3. What is
E
(
X
2
)? What is
E
(
X
2
)?
Example 2
(Example 4b; Functions of a random variable)
.
A product that is
sold seasonally yields a net profit of
b
dollars for each unit sold and a net loss of
l
dollars for each unit left unsold when the season ends. The number of units of
the product that are ordered at a specific department store during any season
is a random variable having probability mass function
p
(
i
)
, i
≥
0. If the store
must stock this product in advance, determine the number of units the store
should stock so as to maximize its expected profit.
Example 3
(Variance)
.
1. If
X
denotes the face that you observe when you
throw a fair 6 faced dice, calculate var (
X
).
2. If
Y
denotes the outcome of an unfair 6faced die where
P
(
Y
= 1) = 1
/
3
,
P
(
Y
= 2) = 1
/
9
,
P
(
Y
= 3) = 1
/
18
P
(
Y
= 4) = 1
/
18
,
P
(
Y
= 5) = 1
/
9
,
P
(
Y
= 6) = 1
/
3
Calculate
E
(
Y
)
,
var (
Y
).
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 Spring '11
 Shakar
 Probability theory, satellite system

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