| ~ wuotv vfv
l ns n e x
| fkwnvkvfwus
x x n l n
d vfpfsvwus
e x l e l n
d
q4
i4
v ~
4
s x e d e x l e x ~ x n x e e y x x n e x n l
GvvxffvvtivcwvsvvvTivsvwvsvwfwn
| wgdjfwffpl ( v w (~
n n g d
e x
wq
ev 4
x
~ vvvvpCovwvvGwf$
36-703
Homework #3
Thursday 16 Feb 2006
1
Fill out the calculations for the Lagrange Inversion Formula noted
in the Notes on Generating Functions document.
LIF-ting
2
Following up on the pentagon problem, consider a nite set of nodes
S = cfw_1, . . . , M
Biological Statistics II
Biometry 3020 / Natural Resources 4130 / Statistical Science 3200
Lab 10
Random and Mixed Effects Models
An automobile manufacturer wished to study the effects of differences between
drivers (factor A) and differences between cars
logdose n dead product
0.1 18 0 A
0.2 16 4 A
0.3 21 7 A
0.4 19 6 A
0.5 16 5 A
0.6 20 10 A
0.7 21 8 A
0.8 18 8 A
0.9 22 15 A
1 24 19 A
1.1 17 13 A
1.2 16 14 A
1.3 21 17 A
1.4 21 19 A
1.5 15 13 A
1.6 15 12 A
1.7 16 16 A
0.1 24 6 B
0.2 22 7 B
0.3 19 6 B
0.4
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Lab Section
April 12, 2016
Biological Statistics II
Biometry 3020 / Natural Resources 4130 / Statistical Science 3200
Lab 8
Multiple logistic regression
Here we carry out a logistic analysis of covariance (ANCOVA) to compare three
different insec
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Lab Section
May 3, 2016
Biological Statistics II
Biometry 3020 / Natural Resources 4130 / Statistical Science 3200
Lab 11 is due May 3rd.
Generalized Additive Modeling
A scientist at the U. S. Environmental Protection Agency is trying to create a
Jin Xing
Your Lab Section
BRTY 3020 / NTRES 4130 / STSCI 2200
April 14, 2016
Exam 2 Spring 2016
150 Total Points
Due by 11:59 pm Thursday April 14, 2016
Code of Academic Integrity
Your own work please!
Principle
Absolute integrity is expected of every Cor
Jin Xing
Lab Section
April 19, 2016
Biological Statistics II
Biometry 3020 / Natural Resources 4130 / Statistical Science 3200
Lab 8
Nonlinear regression
A hospital administrator wishes to develop a regression model for predicting the
degree of long-term
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Your Lab Section
April 28, 2016
Biometry 3020 / Natural Resources 4130 / STSCI 3200
Homework 7
Due on Thursday April 28, 2016
Enzyme Kinetics Data
In an enzyme kinetics study the velocity of a reaction (Y) is expected to be
related to the concent
36-703
Homework #4
Thursday 9 Mar 2006
1
G&S Section 6.2, exercises 79.
Preserving The
Markov Property
2
On the rst day of class, I did a card trick. The participant picked a
number k0 from 1 to 9. The k0 th card in the well-shued deck becomes
the partici
36-703
Homework #4 Solutions
Thursday 20 Mar 2006
1
1.7 Let b = h1 (j) and ar = h1 (ir ). Then,
Preserving the
Markov Property
P(Yn+1 = j | Yr = ir for 0 r n) = P(Xn+1 = b | Xr = ar for 0 r n)
The result follows since Xn is Markovian. If h is not one-to-o
36-703
Homework #8 Solutions
Friday 28 April 2006
1
(a) This is a direct result of Cauchy-Schwarz inequality.
(b) The basic idea is to see that MJ is a martingale. Then apply the
martingale convergence theorem. So, MJ converges to some limit,
M . MJ is a
36-703
Homework #7 Solutions
Thursday 13 April 2006
1
Dene T1 = mincfw_n : Yn b and T2 = mincfw_n > T1 : Yn a and
inductively that
T2k1 = mincfw_n > T2k2 : Yn b and T2k = mincfw_n > T2k1 : Yn a
The interval [T2k1 , T2k ] is called a downcrossing of [a, b]
36-703
Sample Exam
Tuesday 21 Mar 2006
1
Let Y0 = 0 and Yn for n 1 be the sum of n rolls of a balanced,
six-sided die.
Lucky 13
Find
lim Pcfw_13\Yn ,
n
where j\k (j divides k) for integers k and j > 0 means that there is
an integer m such that k = jm.
2
36-703
Solution to nal homework!
Friday 5 May 2006
Please report any typos immediately for a timely response.
1
Call E(Wtn | Wtn1 near un1 , . . . , . . . , Wt1 near u1 ) LHS for short.
Add the quantity Wtn1 Wtn1 into the expected value of the LHS.
Apply
36-703
Homework # 8
Friday 21 Apr 2006
1
Dene H = 1(0,1/2] 1(1/2,1] . Then let
Hjk (t) = 2j/2 H(2j t k).
Then, H0 = 1(0,1] and Hjk for j 0, k = 0, . . . , 2j 1 is called the
Haar basis.
These functions form a complete orthonormal basis for L2 (0, 1). For
36-703
Homework #6 Solutions
Thursday 6 April 2006
Unless otherwise stated, for the remainder of the solutions, dene
Fm = (Y0 , . . . , Ym )
1
We will show EYm = EY0 using induction. m = 0 is obviously true.
For base case m = 1: EY1 = E[E(Y1 | Y0 )] = EY0
36-703
Homework #2
Tuesday 7 Feb 2006
1
Use the basic expected value rules to show the following:
1. If X Y and for both the expected value exists, then EX EY .
2. If A1 , A2 , . . . F are disjoint sets, then
P(Ai ).
Ai =
P
i
Expected
Implications
i
3. Us
36-703
Homework #3 Solutions
Thursday 16 Feb 2006
1
Since we are interested in just T (z), F is the identity function, i.e.
F (x) = x.
So, F (x) = 1. Let u = T (z) G(u) = eu . Then the coecients tn
satisfy
1 n1 nu
u
[z n ]T (z) =
e
n
LIF-ting
Generating f
36-703
Homework #1 Solutions
Thursday 26 Jan 2006
1
Following the example from class, we can write
SB (z) =
=
Pentagon Walk
Revisited
z 2 2z
(z 1)(z 2)(z 2)
z2
4
z
2
z
(1 z)(1 2 )(1
z .
)
2
Solving for a partial fractions expansion of the form
u2
u1
u3
.
36-703
Homework #1
Thursday 26 Jan 2006
1
Let X0 , X1 , . . . be random variables that take values in the set
cfw_A, B, C, D, E. Suppose Xn is the node being visited at time n in the
Pentagon walk we discussed in class. That is, we assume that X0 = A
with
Jin Xing
Your Lab Section
BRTY 3020 / NTRES 4130 / STSCI 2200
2015
May 17, 2016
Exam 3 Spring
150 Total Points
Due by 11:59 pm Monday May 17, 2016
Code of Academic Integrity
Your own work please!
Principle
Absolute integrity is expected of every Cornell s