worksheet 9:
factoring completely
Factor the following expressions completely. You may need to use more than one factoring technique.
1.
2.
3.
4.
4x2 16
t 3 + 3t2 + 4t + 12
4x3 15 + 20x2 3x
ax bx + by ay
5.
6.
(a b )(x + 5) (a b )(10 x)
a 2 (x y ) + 5 (y
AMCS 241: Homework 8
Assigned: Sunday Apr. 30
Due: Sunday May 7 in class (by 9:00am)
Instructions: Follow the guidelines for homework write-ups in the syllabus. If the TAs cannot understand /
read your solution, then you will not receive credit. You are r
AMCS 313 Homework 8
Submitted by Mary Lai Salvaa
April 18, 2017
Exercise 1
Figure 1: Left: Sea surface temperature data in degree Celsius observed on January 10, 2004 in the
southern Atlantic and Indian oceans off the coast of South Africa. As a map, the
AMCS 313 Homework 6
Submitted by Mary Lai Salvaa
March 12, 2017
Variogram
#0.1 INSTALL PACKAGES
i n s t a l l . packages ( " f i e l d s " )
i n s t a l l . packages ( "geoR" )
#i n s t a l l . p a c k a g e s (" RandomFields ")
#i n s t a l l . p a c k a
AMCS 313 Homework 7
Submitted by Mary Lai Salvaa
March 19, 2017
Optimization Problem
Quilt Plot of Data 3
data=read . csv ( " data3 . c s v " , h e a d e r=T)
x=rev ( data [ , 1 ] )
y=rev ( data [ , 2 ] )
z=rev ( data [ , 3 ] )
#1.0 QUILT PLOT OF DATA3
q
AMCS 313 Homework 4
Submitted by Mary Lai Salvaa
February 14, 2017
mean: 0.3704
standard deviation: 1.0648
histogram
The distribution is skewed to the left and does not appear to be normally distributed.
qqplot
Spatial Statistics
Page 2
Towards the tail,
AMCS 241 Homework 3
Submitted by Mary Lai Salvaa
ID No. 1560117
February 21, 2017
1. Consider the Cauchy probability density function:
pY (y) =
d2
c
+ y2
a. Evaluate the ratio c/d.
Solution:
Let Y be a Cauchy random variable. The general form of the Cauch
AMCS 241 Homework 2
Submitted by Mary Lai Salvaa
ID No. 1560117
February 12, 2017
1. A sample space consists of the four points
= cfw_1 , 2 , 3 , 4
and the probabilities of the simple events are
1
1
1
1
P [cfw_1 ] = , P [cfw_2 ] = , P [cfw_3 ] = , P [cf
AMCS 241 Homework 4
Submitted by Mary Lai Salvaa
ID No. 156071
February 28, 2017
1. We say that the joint PDF fXY (x, y) of two random variables X and Y is circularly symmetric
if
p
fXY (x, y) = g(r) , where r = x2 + y 2
Show that if the random variables
AMCS 313 Homework 1
Submitted by Mary Lai Salvaa
January 29, 2017
Effect of AR(1) Autocorrelation Structure on Classical Statistical Inference
Let Y1 , Y2 , , Yn N (Y , 2 ), Cov(Yi , Yj ) = 2 |ij| , i 6= j.
Y1 + Y2 , , Yn
V ar(Y ) = V ar
n
=
=
1
V ar(Y1 +
AMCS 313 Homework 5
Submitted by Mary Lai Salvaa
February 19, 2017
Deriving Exponential Variogram
V ar[Z(s1 ) Z(s2 )] = 2[C(0) C(h)]
h
h i
= 2 1 exp
a
= 2(h)
(
0 , h =n 0
o
(h) =
, h>0
c0 + c 1 exp ha
for some c > 0, c0 > 0, where c0 is the nugget effec
AMCS 241 Homework 5
Submitted by Mary Lai Salvaa
ID No. 156071
March 7, 2017
1. Find the MGF of a triangular distribution defined by
1
|x|
fX (x) =
1
, |x| < a
a
a
Solution:
MX (t) = E[etX ]
Z
|x|
1
dx
=
etx 1
a
a
|x|<a
Z
1
=
etx (a |x|)dx
a2 |x|<a
Z
Z
AMCS 241 Homework 6
Submitted by Mary Lai Salvaa
ID No. 156071
March 28, 2017
1. Let cfw_Xn be a sequence of RVs that converges in probability to a random variable X; that is,
P
X
Xn
Assume that the PDFs fn (x) of Xn are such that, for some N > 0,
fn (x
RC CIRCUIT
OBJECTIVE: To study the charging and discharging process for a capacitor in a simple circuit
containing an ohmic resistance, R, and a capacitance, C.
THEORY: Consider the circuit shown below in Fig. 1:
a
S
b
Vo
R
C
FIGURE 1
1. Charging the capa
1st Sem, A.Y. 20162017
Physics 71.1
Verification of conservation of angular momentum
Table W5: Data for verification of conservation of angular momentum
Case
1
2
Ia (kgm2 )
Ib (kgm2 )
a,i (rad/s)
b,f (rad/s)
Li (kgradm2 /s)
Lf (kgradm2 /s)
% Error
Questio
th
March 15, 2010
Applied Statistics and Probability for Engineers, 5 edition
CHAPTER 9
Section 9-1
9-1
a)
H0 : 25, H1 :
25
Yes, because the hypothesis is stated in terms of the parameter of
interest, inequality is in the alternative hypothesis, and the
CHAPTER
1
SUMMARY
Physical quantities and units: Three fundamental physical quantities are mass, length, and time.
The corresponding basic SI units are the kilogram, the meter, and the second. Derived units for
other physical quantities are products or qu
CHAPTER
10
SUMMARY
S
Torque: When a force F acts on a body, the torque of
t = Fl
(10.2)
S
that force with respect to a point O has a magnitude
given by the product of the force magnitude F and the
S
lever arm l. More generally, torque is a vector T equal
CHAPTER
10
SUMMARY
S
Torque: When a force F acts on a body, the torque of
t = Fl
(10.2)
S
that force with respect to a point O has a magnitude
given by the product of the force magnitude F and the
S
lever arm l. More generally, torque is a vector T equal
Applied Statistics and Probability for Engineers, 5th edition
18 January 2010
CHAPTER 5
Section 5-1
5-1.
First, f(x,y) 0. Let R denote the range of (X,Y).
Then,
f ( x, y)
1
4
18 14 14 18 1
R
a) P(X < 2.5, Y < 3) = f(1.5,2)+f(1,1) = 1/8+1/4=3/8
b) P(X <
Applied Statistics and Probability for Engineers, 5th edition
15 January 2010
CHAPTER 4
Section 4-2
4-1.
a) P(1 X ) e x dx (e x )
1
e1 0.3679
1
2.5
b) P(1 X 2.5)
e
x
dx (e x )
2.5
1
e1 e 2.5 0.2858
1
3
c) P( X 3) e x dx 0
3
4
4
x
x
4
d) P( X 4) e dx (e
Applied Statistics and Probability for Engineers, 5th edition
December 21, 2009
CHAPTER 3
Section 3-1
0,1,2,.,1000
3-1.
The range of X is
3-2.
The range of X is 0,12
, ,.,50
3-3.
The range of X is 0,12
, ,.,99999
3-4.
The range of X is 0,12
, ,3,4,5
3-5.
Applied Statistics and Probability for Engineers, 5th edition
10 February 2010
CHAPTER 7
Section 7-2
7-1.
The proportion of arrivals for chest pain is 8 among 103 total arrivals. The proportion = 8/103.
7-2.
The proportion is 10/80 =1/8.
7-3.
1.01
1.01
P(
Applied Statistics and Probability for Engineers, 5th edition
July 2, 2010
CHAPTER 2
Section 2-1
2-1.
Let a and b denote a part above and below the specification, respectively.
S aaa, aab, aba, abb, baa, bab, bba, bbb
2-2.
Let e and o denote a bit in erro
Applied Statistics and Probability for Engineers, 5th edition
06 February 2010
CHAPTER 6
Section 6-1
6-1.
6-2.
6-3.
6-4.
6-5.
6-6.
6-7.
No, usually not. For example if the sample is cfw_2, 3 the mean is 2.5 which is not an observation in the
sample.
No, i
CHAPTER
6
SUMMARY
S
#
S
S
Work done by a force: When a constant force F acts on
S
a particle that undergoes a straight-line displacement s ,
the work done by the force on the particle is dened to
S
S
be the scalar product of F and s . The unit of work in