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 dimensional
random walk,
Pr(S2n = 0) = Pr( a Binomial (2n, p
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
Problem 6
This problem is the same as arranging n people
# 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)
return(-1+sqrt(1-4*r^2)/(2*r) else return(NA)
# Exhibit 7.
# 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, height=2.5,pointsize=8)
# rwalk contains a simulated random
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 legislators, alumni, and donors.
The purpose of this stude
Name: Ashu Gupta Class: 2016 E-mail: agupta2@imsa.edu
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 relationships with legislators, donors and other outside
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 legislators, alumni, and donors.
The purpose of this stude
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 legislators, alumni, and donors.
The purpose of this stude
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 legislators, alumni, and donors.
The purpose of this stude
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 legislators, alumni, and donors.
The purpose of this stude
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 legislators, alumni, and donors.
The purpose of this stude
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 legislators, alumni, and donors.
The purpose of this stude
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 legislators, alumni, and donors.
The purpose of this stude
# 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 temperature for two years.
data(tempdub)
tempdub1=ts(c(tempdub
# Exhibit 4.2
win.graph(width=4.875, height=3,pointsize=8)
data(ma1.2.s)
plot(ma1.2.s,ylab=expression(Y[t]),type='o')
# An MA(1) series with MA coefficient equal to -0.9 and
# of length n=100 can be simulated by the following command
set.seed(12345) # in
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 (A2 ) .75 P (A3 ) .80 P (A4 ) .85. Goal: Minimize P (A1
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) = 1/5,
mY (4) = 2/5,
mY (5) = 1/5.
(b) The possible valu
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 following, i.e., by symmetry,the
integrand is an odd functio
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 (X )|
m(x)
=
|xE (X )|
= Pr(|X E (X )| ).
Problem 2: C
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
dy
(1 + 2 )
(1 )(2 ) 0
t 1 + 2 1
=
=
(I)
where (I) is
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.
FW (w) = Pr(W w) = Pr(aX + b w)
= Pr(aX w b)
Pr(X (w b)
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 k )!k !
(b) Let pN denote the probability X = n12 , gi
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 could play the game, it would be favorable no matter
how mu
Stat 241/541 Homework 5 Solution
Section 3.1: 4
4. At this writing, 37 Presidents have died. The probability that no two
people from a group of 37 (all of whom are dead) died on the same day
is
365 364 (365 37 + 1)
0.15 .
36537
Thus, the probability that