CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Assignment 2
(Due Sep 22, 2011)
1. Problem 3.3 in Ross: Let S=cfw_1,2,3,4,5,6,7, E=cfw_1,3,5,7, F=cfw_7,4,6, G=cfw_1,4.
Find
a. EF
b. E FG
c. EGc
d. EFc G
e. Ec(F G)
f. EG FG
2. (Problem 3 fro
CE 93 Fall 2011
Hansen, Liu, Seelhorst
CE 93 Fall 2011 Homework 4 Solutions
1. The daily water levels (normalized to the respective full condition) of two reservoirs A
and B are denoted by two random variables X and Y having the following joint PDF:
a.
b.
CE93_Engineering Data Analysis
Solution to HW2
1. Problem 3.3 in Ross.
a. EF = cfw_7
b. E U FG = cfw_1,3,4,5,7
c. EGc = cfw_3,5,7
d. EFc U G = cfw_1,3,4,5
e. Ec (F U G) = cfw_4,6
f. EG U FG = cfw_1,4
2. a.
(
)(
(
(
)(
)(
E= (
(
)(
)(
)(
)(
)(
)(
)(
)(
)(
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Assignment 3
(Due Oct 6, 2011)
1. A gross polluter detection system consists of two sensors, A and B, and is used to identify
motor vehicles that are gross pollutersvehicles whose emissions of
CE 93 Fall 2011 Hansen, Liu, Seelhorst
Midterm Solution
1. AQI values, sorted from lowest to highest
a. Construct a histogram of these data
Anything similar to one of these will work. The number of bins shouldnt be too small or
too large.
Histogram with 1
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Assignment 6 Solutions
Due November 17, 2011
1. (15 points)
The average rate of accidents is about 0.028 / day or 0.028*7 = 0.196 / week. Using the poisson
pmf, where x = # accidents in a week
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Solution to Assignment 7
1. [15 points]
Two-sided hypothesis test: H0: = 8.2 vs. H1: 8.2
(use the normal distribution because variance is known)
p-value = 2 [1 (3.3204)] = .0010
This is smalle
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Solution to assignment 5
1. (20 points) X is a normal random variable with
(
a.
)
(
(
(
b.
(
)
)
) (Normalize the variable)
)
, compute
(
)
(
)(
CDF of Z)
(
( )
( ) (Property of symmetry)
(
)
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Solution to HW 3
1. (40 points) Given are:
D: detect
DA: detect by A
DB: detect by B
G: gross polluter
System A:
,
,
System B:
,
,
,
a. Find P(G|Dc) for A only or say P(G|Ac). Use Bayes Theore
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Assignment 7
Due Dec 1, 2011
1. Problem 8.4 in Ross.
2. Problem 8.24 in Ross performing both a two-sided and a one-sided hypothesis test. If you
were testing this product for use in constructi
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Assignment 6
Due November 17, 2011
1. The table below shows the intervals (in days) that elapsed between thirty-seven consecutive
fatal car accidents in a certain town. Assuming that the numbe
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Assignment 5
(Due Nov 3, 2011)
1. X is a normal random variable with
a. P(X>5)
b. P(2<X<15)
c. P(X<3)
d. x such that P(X<x) 0.3192
, compute
2. The drainage from a community during a storm is
CE93_Engineering Data Analysis
Hansen, Liu, Michael, Fall 2011
Assignment 4
Due October 20, 2011
1. The daily water levels (normalized to the respective full condition) of two reservoirs A and B are
denoted by two random variables X and Y having the follo
CE93 Engineering Data Analysis
Spring 2011 Midterm
11:10am-12:00pm, Mar15, 2011
You have 50 minutes to complete the midterm exam.
There are 4 questions; points are indicated for each question part. There are a total of 100 points.
Please be sure to write