Unformatted text preview: CE93Engineering Data Analysis Mark Hansen, Fall 2009 Assignment 3 Solutions
1. Problem 3.5 in Ross.
a) Outcomes:
b) {1100,1101,1110,1111,0011,0111,1011}=
c) {0000,0101,0001,0100}=
2. Problem 3.12 in Ross.
P(E)=0.9, P(F)=0.9
Show that the
is at a minimum when event E and event F overlap as little as possible, i.e.
. Therefore the minimum that
can be is 10.2=0.8. when is at a maximum when event E and event F overlap as much as possible, i.e.
when
. Therefore the maximum that
can
be is 10.1=0.9.
Generally,
↔
, where S is the sample space. ↔ 1 CE93Engineering Data Analysis Mark Hansen, Fall 2009 3. Container ships direction and speed.
a. Draw the sample space for the ships’ speeds and directions. b. Identify the following events within the sample space in (a).
i. ii. iii. ; ; ; CE93Engineering Data Analysis iv. , and v. . c. Make new drawings to show the following:
i. ; Mark Hansen, Fall 2009 CE93Engineering Data Analysis ii. , and iii.
Among ,
and Mark Hansen, Fall 2009  null.
, and , which pairs of events are mutually exclusive? are mutually exclusive because their spaces do not overlap. Alternatively, you can use the polar coordinate system to express the sample
space or each event. For example, sample space in the polar coordinate is as
below: 5. Travel between cities A and B
a. Sample space of travel conditions Event E includes situations 1, 2, 3, 4, 5, 6, 7, 9, 12 in S.
b.
c.
Travel from city A to city B is not available when at least one among Highway 1, Tunnel and
Highway 2 is closed and Highway 3 is closed. CE93Engineering Data Analysis Mark Hansen, Fall 2009 6. Code in Assignment 3 solution_q6.
S S5 A A B B C, S C C, S A B AC BC CC C), S AB C, S A C B C, S1=find((density>2430strength>55)ratio>25000)
S2=find(density>2430(strength>55ratio>25000))
S3=find((density>2430&strength>55)ratio>25000)
S4= find((density>2430 ratio>25000)&( strength>55 ratio>25000))
S5= [4;30;39] (< complement of S1)
S6= find(density<=2430& strength<=55& ratio<=25000)
compare.m
%% comapre two vectors and return comparison result.
%% Two vectors are same When the number of matches of two vectors are equal to the length of
each vector
function [result]=compare(a,b)
myCount=0; % variable to record number of matches
result='0';
for n=1:length(a),
myCount=myCount+sum(b==a(n));
end
if((myCount==length(a))&(myCount==length(b)))
result='two vectors are same';
else
result='two vectors are different';
end
If we apply compare.m for (S1,S2), (S3,S4) and (S5,S6), then
The results are as follows:
>> compare(S1,S2)
ans =
two vectors are same >> compare(S3,S4) CE93Engineering Data Analysis
ans =
two vectors are same >> compare(S5,S6)
ans =
two vectors are same Another code to find matches:
B=0
for n=1:length(S1),
for m=1:length(S2),
if S1(n,1)S2(m,1)==0
B=B+1;
else B=B+0;
end; end; end; Mark Hansen, Fall 2009 ...
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 Cartesian Coordinate System, Coordinate system, Polar coordinate system, Mark Hansen, CE93Engineering Data Analysis

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