Mathematical Statistics
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Chapter 5 - Estimation
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Probability and Statistics - Homework 9
Problem 1
The scores on an entrance exam(x) and the GPA upon graduation (y) for 10 randomly
selected students of a certain university are
x 355 361 402 365 375 404
y 3.66 3.49 3.86 3.24 3.55 3.92
(a)[12 points] Assu
Probability and Statistics - Solution to Homework 8
1. Solution:
(a) For the power function of Test1:
W hen 0 < 0.95,
( + 1) 0.95
= + 0.05;
1
C () = P (X1 > 0.95) =
W hen > 0.95,
C () = P (X1 > 0.95) = 1
For the size of Test1:
C = sup C () = 0.05
=0
(b)
Probability and Statistics - Homework 9
1.) The scores on an entrance exam (x) and the GPA upon graduation (y) for 6 randomly selected students
of a certain university are
x 355
y 3.66
361
3.49
402
3.86
365
3.24
375
3.55
404
3.92
(a) Assume that yi = + xi
Probability and Statistics, 2015
Homework 7
1. Suppose X1 , Xn be i.i.d from N (0, 2 ).
(a) Find the MLE for 2 . Is it unbiased?
(b) Compare the MLE for 2 with the sample variance Sn2 and discuss
which one is better by calculating its MSE.
2. Let X1 , , X
Probability and Statistics - Homework 6
1) Suppose the distribution of Y , conditional on X = x, is uniform distribution U (x3, x)
and that the marginal distribution of X is uniform(0,1). Calculate cov(X, Y ), E(Y )
and var(X|Y ).
2) Suppose (X1 , , XN )
Probability and Statistics - Homework 8
1. Let X1 and X2 iid U (, + 1). For testing H0 : = 0 vs HA : > 0. We have two competing tests:
Test 1: Reject H0 if X1 > 0.95
Test 2: Reject H0 if X2 > C.
Then complete the following tasks.
(a) Calculate the size an
Derivatives and Risk Management
Fall 2016
Assignment 5
Due: 28/11/2016
Exercise 1:
A company has a position in bonds worth $6 million. The modified duration of the portfolio is 5.2 years.
Assume that only parallel shifts in the yield curve can take place
General guidelines for exams in WISEflow FLOWassign (WOAI and WOA)
In connection with digital exams, it is the students own responsibility to bring a fully functioning
computer that is updated and meets the system requirements (PC or Mac). You should not
FINANCIAL STATEMENT
ANALYSIS & VALUATION
Third Edition
Peter D.
Easton
16114
Mary Lea
McAnally
Gregory A.
Sommers
Xiao-Jun
1/20
1
Zhang
Module 1:
Framework for
Analysis and Valuation
2
Structure of module 1
Four Steps in Financial Statement Analysis and V
Financial Statements
1Balance Sheet: Mirrors the Accounting Equation
Assets = Liabilities + Equity
Uses of funds = Sources of funds
Assets are listed in order of liquidity
Liabilities are listed in order of maturity
Equity consists of Contributed Capital
Module 9:Inter-corporate Entities
1Accounting Treatment and Financial Statement Effects
2Passive Investments:
Market MethodInitially record at purchase price (fair market value on
purchase date)
During holding period, investment is recorded at current mar
Equity Recognition and Owner Financing
Total stockholders equity is divided into two components:
1. Contributed capital(
) - proceeds received
by the issuing company from original stock issuances, net of the amounts paid to
repurchase shares of the issuer
logo
Inditex
Yunkai Weng
Bingjie Hao
Danni Xu
Jinfeng Bao
Introduction
Contents
SWOT Analysis
Accounting
Financial Analysis
2
01
Part One
Introduction
3
Introduction
Inditex is a spanish
multinational colthing
comany and it is the
biggest fashion retailer
Probability and Statistics - Solution to Homework 6
1
0 +1 1
=
2
2 ,
E=
(X)
According to Law of Iterated Expectations,
E (Y) =
E E (Y X )
+
= E yf (y x) dy
x 1
= E
ydy
x 3 3
3
= E x
2
1 3
2 2
=
= 1
f=
(x, y) f (y x) f (x)
1
1
3
=
=
E (xy) =
+
=
1
Probability and Statistics - Solution to Homework 7
1. Solution:
(1) The likelihood function of the sample Xn is given by
2
n
L( |X ) =
n
Y
f (Xi , 2 )
i=1
n
1
= (2 2 ) 2 e 22
Pn
i=1
Xi2
Hence, the log-likelihood function is
n
n
1 X 2
2
l( |X ) = ln(2 ) 2
Chapter 7
Convergence and Limit Theorems
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Chapter 7 Abstract
This chapter will introduce some basic analytic tools for
asymptotic analysis or large sample anal
Chapter 3
Random Variables and Univariate
Probability Distributions
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Review of Chapter 2
Definition: -Alge
Chapter 4
Important Probability
Distributions
Fall 2015
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4.1 Introduction
Main Goal: We introduce a variety of discre
Chapter 2 - Foundation of
Probability Theory
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Abstract
Probability theory is the foundation of statistical
Chapter 5 (Contd)
Multivariate Probability
Distributions
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Brief Review
Joint, Marginal, and Conditional PMF/PDF:
fY |X (y|x) =
fXY (x, y)
fX (x)
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if fX
Chapter 8
Parameter Estimation and
Evaluation
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8.1 Introduction
Problem: Consider a random sample X1, , Xn from
some population distribution fX (x; 0) with unk
Chapter 5 (Contd)
Multivariate Probability
Distributions
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Brief Review
Definition: Joint Cumulative Distribution Function. The function of two real variables,
Mathematical Statistics
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Chapter 9 - Two-Sample Inferences
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C
Mathematical Statistics
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Chapter 6 - Hypothesis Testing
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Xiamen University
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Clo
Chapter 6
Introduction to Sampling Theory
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Abstract
Chapter 6 - Introduction to Sampling Theory
In the previous chapters, we have discussed theory and
methods
Chapter 9 - Hypothesis Testing
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Abstract of Chapter 9
In Chapter 6, we learned the hypothesis tests based on normal, 2, t, and F di
Mathematical Statistics
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Chapter 7 - Inferences Based on the
Normal Distribution
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Outline of Cha
Chapter 5
Multivariate Probability
Distributions
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Abstract
Chapter 5 - Multivariate Probability Distributions
Before: We focused Single random variables (X) CD