In pedigree analysis, when a trait is rare, this means the mutant allele responsible for the trait is present at low frequency in the population. So people marrying into the family are assumed to be homozygous dominant for pedigrees that exhibit recessive
AMSB 16.01 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. Please provide complete solutions for full credit. Good luck!
1. Consider
AMS316 Homework #1 (due Sept 14, 2011)
This problem set is used as a self-test of your background on AMS311 and AMS315, it doesn't represent the format or level of homework in AMS316. The grade of homework 1 will be not counted for final grade. 1. Let the
AMS316 Sample Midterm
This is the AMS316 miderm in fall 2010. 1. Suppose we have a seasonal seris of monthly observations cfw_Xt , for which the seasonal factor at time t is denoted by cfw_St . We further assume that the seasonal pattern is constant throu
AMS316 HW3
(Due Oct 24, 2011) In the following equations, cfw_Zt is a discrete-time, purely random pro2 cess such that E(Zt ) = 0, Var(Zt ) = Z , and successive values of Zt are independent so that Cov(Zt , Zt+k ) = 0, k = 0. 3.1 Show that the ac.f of th
AMS316 Homework 2
2.1
The following data show the coded sales of company X in successive 4-week periods over
1995-1998.
1995
1996
1997
1998
I
153
133
145
111
II
189
177
200
170
III
221
241
187
243
IV
215
228
201
178
V
302
283
292
248
VI
223
255
220
202
VI
needs to be any obvious particular problem the consideration. page_30there adapted to the discontinuities inunderdata? If so, what does this mean? Are Page you Do 30 make sense context? Have the of the variables? Does itunderstand theto transform any `rig
AMS316 Homework#2
1. The following data show the coded sales of company X in successive 4-week periods over 1995-1998.
1995 1996 1997 1998 153 133 145 111 189 177 200 170 221 241 187 243 215 228 201 178 302 283 292 248 223 255 220 202 201 238 233 163 173
This le is made by Prof Junhui Wang.
Some Basic Results in Probability & Statistics
Linear Algebra
Probability
Random Variables
Common Statistical Distributions
Statistical Estimation
Statistical Inference about Normal Disbributions
2
Linear Algebra
AMS316 Homework #1 (due Sept 12, 2012, in class)
This problem set is used as a self-test of your background on AMS311 and AMS315, it
doesnt represent the format or level of homework in AMS316. The grade of homework 1
will be not counted for nal grade.
1.
AMS316 HW3
In the following equations, cfw_Zt is a discrete-time, purely random pro2
cess such that E (Zt ) = 0, Var(Zt ) = Z , and successive values of Zt are
independent so that Cov(Zt , Zt+k ) = 0, k = 0.
3.1 Show that the ac.f of the second-order MA
AMS316 HW4
(Due Nov 16, 2011) 1. Find the ac.f of the first-order AR process defined by Xt - = 0.7(Xt-1 - ) + Zt Plot (k) for k = -6, -5, ., 0, +1, ., +6 (Remark: You can plot in Excel for convenience, if you want). 2. Assume the AR(2) process Xt = 1 Xt-1
AMS316 HW5
(Due Nov 30, 2011) 1. Following the procedure I have done in class, show that the ACFs of the ARM A(1, 1) model, Xt = Xt-1 + Zt + Zt-1 , is given by (1) = (1 + )( + )/ 1 + 2 + 2 (k) = (k - 1), k = 2, 3, . 2. For the model (1 - B)(1 - 0.2B)Xt =
AMS316 HW6
(Due Dec 12, 2011) 1. Consider the AR(1) process, Xt = + Xt-1 + Zt , where Zt are i.i.d. standard normal random variables. Derive the least square estimates for and by minimizing
n
S(, ) =
t=1
Xt - - Xt-1 .
2
2. For the MA(1) model given by Xt
An Introduction to R
Notes on R: A Programming Environment for Data Analysis and Graphics Version 2.13.2 (2011-09-30)
W. N. Venables, D. M. Smith and the R Development Core Team
Copyright Copyright Copyright Copyright Copyright
c c c c c
1990 W. N. Venabl
AMS316 Final in 2010 (2-hour exam)
Assume that zt are independent and identically distributed normal random variables with mean 0 and variance 2 . 1. Consider the process xt = a + bt + ct2 + st + yt , in which st is a deterministic process satisfying st =
The Three Kingdom Period
Terms: The Three Kingdoms (Kogury, Paekche, Silla), Wa and Mimana, horse rider theory,
warrior aristocracy, centralized monarchical states, tributary system, Sui-Tang invasions to
Kogury, Tang-Silla alliance
1. The unification of
AMS316 HW3
In the following equations, cfw_Zt is a discrete-time, purely random process such that E(Zt ) = 0, Var(Zt ) = Z2 , and successive values of Zt are
independent so that Cov(Zt , Zt+k ) = 0, k 6= 0.
3.1 Show that the ac.f of the second-order MA p
AMS316.01
Midterm Exam 1
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. Please provide complete solutions for full credit. Good luck!
1. Plea
TIME-SERIES
FORECASTING
c 2000 by Chapman & Hall/CRC
TIME-SERIES
FORECASTING
Chris Chatfield
Reader in Statistics
Department of Mathematical Sciences
University of Bath, UK
CHAPMAN & HALL/CRC
Boca Raton London New York Washington, D.C.
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