HW#10Solutions
AngandTang:6.2,6.6,6.9,6.13
Due:Th12/1/2011
6.2
(a) Since x = 65, n = 50, = 6, a 2-sided 99% interval for the true mean is given by the limits
6
65 k0.005
50
<>0.99 = (65 2.58
6
, 65 + 2.58
50
6
)
50
= (62.81, 67.19) (in mph)
6
2
(b) Requ
HW 9
Ang and Tang: 3.33, 3.51, 3.57, 4.15, 4.17,4.20
Due Thurs 11/17/2011
3.33
Let J1 and J2 denote the events that Johns scheduled connection time is 1 and 2 hours, respectively, where P(J 1) =
0.3 and P(J2) = 0.7. Also, let X be the delay time of the fl
HW #7 Assignment
Due Thurs Oct 27, 2011
Problem #1:
Let X take the values 0, 1, 2, 3, 4 and 5 with probabilities p0 , p1 , p2 , p3 , p4 and p5 . Find the
probability mass function of Y = ( X 2)2
Y takes on the values 4,1,0,1,4,9 corresponding to each X va
HW #6 Solutions
Ang and Tang: 3.30, 3.34, 3.54, 3.58, 3.59
Due: 10/20/2011
3.30
Given: both I and N are Poisson processes, with I = 0.01/mi and N = 0.05/mi. Hence, along a 50-mile section of
the highway, I and N have Poisson distributions with respective
HW #5 Solutions (Fall 2011)
Assigned problems
Ang & Tang: 3.7, 3.14, 3.18, 3.19, 3.26
Not checked
3.7
NOTE: in the problem the range of x is x > 10 not x > 0
(a) The mean and median of X are 13.3 lb/ft2 and 11.9 lb/ft2, respectively (as done in
Problem 3-
HW #3 Solutions (Fall 2011)
Assigned problems
Ang & Tang: 2.41, 2.42, 2.58, 3.8, 3.9, 3.12
2.41
Let L, N, H denote the event of low, normal and high demand respectively; also O and G
denote oil and gas supply is low respectively.
(a)
Given normal energy d
HW #2 Solutions (Fall 2011)
Assigned problems:
2.24, 2.37, 2.48, 2.64, 2.65
2.24
(a)
Let A, B denote the event of the respective engineers spotting the error. Let E denote the event that
the error is spotted, P(E) = P(AB)
= P(A) + P(B) P(AB)
= P(A) + P(B)
HW #1 Solutions (Fall 2011)
Assigned problems:
2.5, 2.10, 2.18, 2.19, 2.23
2.5 (Confirmed)
(a)
Locations Locations
Load at B Load at C
of W1
of W2
MA
Probability
E1
0
0
0
B
500
0
5,000
0.045
C
0
500
10,000
0.075
B
200
0
2,000
0.05
B
B
700
0
7,000
0.075
X
CE 408/Johnson
Homework Format Instructions
The problems you turn in must conform to the standards of good engineering practice as outlined
below and as in the example on the next page. Nonconforming homework will not be graded.
1. Homeworks should be wri
Formulas
( A B ) C = AC BC
( AB ) C = ( A B ) ( A C )
E1 E2 = E1 E2
E1 E2 = E1 E2
P( A) = 1 P( A)
P( A B) = P( A) + P(B) P( AB)
n
P( A) =
P( A E i) P(E i)
P(E i A) = -P( A)
P( A E j ) P(E j )
j=1
n
P( AB)
P( A B) = -P(B)
P( A BE j ) P(E j
P( A B) =
B)
j=
2
C iapter 2 Fundamentals of Probabdity Models
2.3 Mathematics of Probability
53
For three events, the multiplication rule would give,
pi )
and
P(fr)
7
7
At the intersection, if a vehicle is definitely makine a turn, the probability that it will be a righ
2%
Chapter 1, Roles of Probability and Statistics in Engineering
.\ Survey of Progress in House Building. Building iich
(saIl Management. VoL 7(4). April 1969, pp. 88 9!
(san. WI . and Snodgrass. DV. Machine Stress Rated Lumber:
h.d knae to Design, Journa
I
Roles of Probability and
Statistics in Engineering
11
INTRODUCTION
engineers, it is im
In dealing with real world problems, uncertainties are unavoidable. As
major sources of uncertainty in engineering.
portant that we recognize the presence of all
that
CE 408/Johnson
Computer Assignment #3
Parameter Estimation and Functions of a Random Variable
Purpose
Thus far, we have dealt with the problem of characterizing the behavior of a random variable. The
next logical problems to be solved are how, given a set
CE 408/Johnson
Computer Assignment #2
Conditional Probability
Write MATLAB programs to solve the following problems. You may work together in groups of at most 3. (Turn in
one copy of your results.)
Applying the knowledge you gained in the last computer a
CE 408/Johnson
Computer Assignment #1
Write MATLAB programs to solve the following problems. You may work together in groups of at
most 3 (turn in just one completed assignment for your group).
Problem 1: Using the functions discussed in 6.0 of the MATLAB