Stat 241/541 Homework 6 Solution
Problem 1:
Let P0 be the probability that the random walk never returns to 0. Let E be the
event that the random walk returns to 0 nitely often. Then for our one dimen
HW3 Solution
1
1.1
Section 3.1
Problem 3
For each bit, two choices (either 0 or 1) are available. Therefore for a word consisting a string of 32 bits, 232 different possibilities are available.
1.2
Pr
# Chap7.R
# Below is a function that computes the method of moments estimator of
# the MA(1) coefficient of an MA(1) model.
estimate.ma1.mom=function(x)cfw_r=acf(x,plot=F)$acf[1]; if (abs(r)<0.5)
ret
# Exhibit 3.1
# time(rwalk) yields a time series of the time epoches when the random walk was sampled.
data(rwalk)
model1=lm(rwalk~time(rwalk)
summary(model1)
# Exhibit 3.2
win.graph(width=4.875, heig
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
Name: Ashu Gupta Class: 2016 E-mail: [email protected]
Briefly answer the following questions:
1. What you know about SCIA and why do you believe it is important to the IMSA community?
SCIA improves re
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
The Student Committee for IMSA Advancement (SCIA)
Application for 2013-2014
Mission Statement: As the Student Committee for IMSA Advancement, we work to advance
IMSA by building relationships with leg
S&DS 241 / 541 and Math 241
Homework 3
due Sept. 27, 2017
Guidelines
Please read and follow all the guidelines in Winstons Sept. 19 Homework guidelines
announcement on Canvas.
Problems
Chapter 2, Exe
S&DS 241 / 541 and Math 241
Homework 1
due Sept. 13, 2017
Guidelines
Please do not write your name on the front of your homework. Write your Yale SIS
ID on the front of the first page. Write your nam
# chap9.R
library(TSA)
# Exhibit 9.1
data(color)
m1.color=arima(color,order=c(1,0,0)
m1.color
# Exhibit 9.2
# append 2 years of missing values to the tempdub data as we want to forecast
# the tempera
HW1 and HW2 Solution
1
1.1
HW1
Problem 16
Assume Aj , j = 1, 2, 3, 4 , stands for the event that a soldier lost one eye, lost one ear, lost one hand and lost one leg respectively. Then,
P (A1 ) .70 P
STAT 241/541 Homework 1 Solution
Prepared by James Hu
Problem 1: Ch1.2:14
(a) The possible values that Y may take are 2, 3, 4 and 5. Therefore, the
distribution function of Y is
mY (2) = 1/5,
mY (3) =
STAT 241/541 Homework 12 Solution
Prepared by James Hu
Problem 1: Ch 10.3:10
a) Since the density function is an even function over the range (, +),
the mean is 0. This can also be seen from the follo
STAT 241/541 Homework 11 Solution
Problem 1: Ch 8.1:14
W.L.O.G., lets assume X is discrete and has distribution function m(x) , then
|x E (X )|m(x)
E (|X E (X )|) =
x
|x E (X )|m(x)
|xE (X )|
m(x)
|xE
STAT 241/541 Homework 10 Solution
Problem 1:
Using the convolution method,
fX (t y )fY (y )dy
fX +Y (t) =
0
t
1
2 2 1 y
(t y )1 1 e(ty)
y
e
dy
(2 )
0 (1 )
t
1 +2 1 +2 1 t (1 + 2 )
(t y )1 1 y 2 1
t
e
STAT 241/541 Homework 9 Solution
Section 5.2 : 18, 28, 34
18 What we need is to nd FW (w), where W = aX + b, because FY and FZ
can be obtained by substituting a = 1 and b = 0 into FW , respectively.
F
STAT 241/541 Homework 8 Solution
Section 5.1 : 10, 24, 32, 44
10 (a) The probability of X = k is:
Pr(X = k ) =
=
N
k
N k N n1
n1 k n2 k
N
N
n1 n2
(N n1 )!(N n2 )!n1 !n2 !
N !(N n1 n2 + k )!(n1 k )!(n2
STAT 241/541 Homework 7 Solution
Prepared by James Hu
Section 6.1: 20, 30, 36
20 (a) The expected value of winnings:
1
12 2
1
2+
2 +
2
2
2
= 1 + 1 + 1 +
E (X ) =
3
23 +
=
This means that if we coul
S&DS 241 / 541 and Math 241
Homework 2
due Sept. 20, 2017
Guidelines
Please do not write your name on the front of your homework. Write your Yale SIS
ID on the front of the first page. Write your nam