ASSIGNMENTS 3 OF AMS 516
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Ex 4.4 Proofs: Since
and
We have
Ex 4.5 Proofs: Since
We have
Since
Where
Hence
and
Ex 2.7 Solutions:
(a) Sample covariance matrix
(b) From exercise 2.6(b), we have
Solutions to Assignments 1 of AMS 516
Problem 2.4 Solution:
(a) Define
Suppose that
We have
Hence
(b) Since
is non-singular, we have that
(c) Define
exists.
we have
Define
we have
Since
We have
Hence
Lecture 2. Statistical Inference:
Confidence Interval
Scenario 1: Review of Confidence Interval for One Population
Mean when the Population is Normal and the Population
Variance is Known
Motivation &
3.6
(c) The test results are:
Stock
p-value
AAPL
0.021
ADBE
0.054
ADP
0.157
AMD
0.004
DELL
0.007
GTW
0.060
HP
0.969
IBM
0.091
MSFT
0.027
ORCL
0.11
Therefore we should reject the null hypothesis for AA
Power of the test & Likelihood Ratio Test
Power Calculation (Inference on one population mean)
Likelihood Ratio Test (one population mean, normal
population)
Truth
H0
Decision
Ha
Type II error
H0
Type
Inference on One Population Mean
Hypothesis Testing, Pivotal Quantity Approach
Scenario 1. When the population is normal, and the population variance is
known
Data : X 1 , X 2 , X n
i .i . d .
~ N (
AMS516.01
Practice Midterm Exam 2
Fall 2014
Name: _ ID: _ Signature: _
Instruction: This is a close book exam except for one 8x11 formula sheet (double sided). The exam goes
from 1:00pm-2:20pm. Pleas