550.430 Introduction to Statistics
Spring 2010
Naiman
Homework #2
Due Monday Feb 13th
(1) Chapter 7 #24
(2) Chapter 7 #35
(3) Chapter 7 #37
(4) Suppose we estimate the mean income
μ
for people living in some city using an esti-
mator ˆ
μ
with the property that
ˆ
μ
∼
N
(
μ, σ
2
)
.
(a) What is the probability that ˆ
μ < μ
+
.
75
σ
?
(b) What is the probability that ˆ
μ > μ
+ 1
.
25
σ
?
(c) What is the probability that
μ
+
.
60
σ <
ˆ
μ < μ
+
.
75
σ
?
(d) What is the probability that
μ
-
.
60
σ <
ˆ
μ < μ
+
.
75
σ
?
(e) What is the probability that
|
ˆ
μ
-
μ
|
< σ
?
(5) Suppose we estimate the mean height of
μ
for people living in some city using an
estimator ˆ
μ.
We also estimate the standard deviation
σ
ˆ
μ
of the estimator using an
estimator denoted by
s
ˆ
μ
.
Assume that the quantity
ˆ
μ
-
μ
s
ˆ
μ
is distributed as Student’s t with 10 degrees of freedom.
(a) What is the probability that ˆ
μ > μ
+ 1
.
812
s
ˆ
μ
?
(b) What is the probability that
|
ˆ
μ
-
μ
|
<
1
.
812
s
ˆ
μ
(6) (Use of Chebychev’s inequality) Consider estimation of a population mean
μ
whose
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- Fall '11
- Naiman
- Statistics, Probability, Standard Deviation, Variance, Probability theory
-
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