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EXAM 1 – FORM A
STAT 211
SPRING2004
Future recognition from surface models of complicated parts is becoming increasingly important in the development
of efficient computer-aided design (CAD) systems. The following is the number edges of a part and the recognition
time (in seconds) recorded (both in logs and real observation) to examine the relationship between them.
Log(EDGES)
1.10
1.50
1.70
1.90
2.00
2.10
2.20
2.30
2.70
2.80
3.00
3.30
3.50
3.80
4.20
4.30
Log(TIME)
.30
.50
.55
.52
.85
.98
1.10
1.00
1.18
1.45
1.65
1.84
2.05
2.46
2.50
2.76
EDGES
3.00
4.48
5.47
6.69
7.39
8.17
9.03
9.97
14.88 16.44 20.09
27.11 33.12 44.70 66.69 73.70
TIME
1.35
1.65
1.73
1.68
2.34
2.66
3.00
2.72
3.25
4.26
5.21
6.30
7.77
11.70 12.18 15.80
80
5
16
15
4
60
3
40
2
20
16
0
1
-20
0
16
16
Log(edges)
Log(time)
N=
N=
16
16
EDGES
TIME
Statistics
Log(edges)
16
Log(time)
16
EDGES
16
Mean
2.650
1.356
21.9328
5.2260
Median
2.500
1.140
12.4270
3.1293
Std. Deviation
N
Valid
TIME
16
.9654
.7800
22.08033
4.42187
Skewness
.303
.471
1.497
1.358
Minimum
1.1
.3
3.00
1.35
Maximum
4.3
2.8
73.70
15.80
Percentiles
25
1.925
.625
6.8617
1.8849
75
3.450
1.997
31.6147
7.4001
Answer questions 1 to 5 using the information above.
1.
Which of the following should be used to compare the variability of the number of edges (EDGE) and
recognition time (TIME)?
(a) Standard deviation
(b) Range
(c) Coefficient of variation
because those datasets have different units
(d) Interquartile range
(e) All of the above
STAT 211
EXAM 1 – FORM A
SPRING2004
2.
What proportion of data is higher than its median for the log(edges) data?
(a) 0.1
(b) 0.3
(c) 0.5
there are 8 observations larger than the median (=2.5) out of 16
(d) 0.7
(e) 0.9
3.
What is the interquartile range for edges data?
(a) 1.372
(b) 1.525
(c) 5.5152
(d) 24.753 =upper quartile-lower quartile=31.6147-3.45
(e) 70.7
4.
Which of those data sets are negatively skewed?
(a) Edges
(b) Time
(c) Log(edges)
(d) Log(time)
(e) None of them
Either by looking at SK (skewness) measure or boxplots
5.
Which of the following is the difference between largest 25% of edges and largest 25% of log(edges)?
(a) 1.453
(b) 1.525
(c) 24.753
(d) 28.1647 =31.6147-3.45
6.
In a sample of n=50 observations, the density of a histogram class interval of width 2 is 0.10. Which of the
following is the frequency for the same interval?
(a) 0.10
(b) 2
(c) 10
because density=(frequency/total data)/interval width where 0.10=(frequency/50)/2
(d) 20
(e) 50
7.
What is the reliability of the parallel system of 4 components with component success probabilities 0.9, 0.8, 0.8,
0.9?
(a) 0.0016
(b) 0.4816
(c) 0.5184
(d) 0.9984
(e) 0.9996
=1-(1-0.9)(1-0.8)(1-0.8)(1-0.9)
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider
observing the direction for each of the three successive vehicles. There are 27 outcomes in the sample space. Let A
be the event that all three vehicles go in the same direction, B be the event that all three vehicles turn in different
directions, and C be the event that exactly 2 of the three vehicles turn right. The following are the outcomes in those
indicating (1st car, 2nd car, 3rd car).
A={(R,R,R),(L,L,L),(S,S,S)}
B={(L,R,S),(L,S,R),(S,L,R),(S,R,L),(R,L,S),(R,S,L)}
C= {(R,R,L),(R,R,S),(L,R,R),(S,R,R),(R,L,R),(R,S,R)}
Answer questions 8 to 12 using this information.
8.
Which of the following are mutually exclusive?
(a) Only A and B
AB={}
(b) Only A and C
AC={}
(c) Only B and C
BC={}
(d) All of the above
STAT 211
9.
EXAM 1 – FORM A
SPRING2004
Which of the following is P(A | B)?
(a) 0 = P(AB)/P(B)=0/(6/27)
(b) 0.2
(c) 0.3333
(d) 0.4
(e) 0.6667
10. Which of the following is the P(C)?
(a) 0.1111
(b) 0.2222 =6/27 there are 6 outcomes in C out of all 27 in the sample space
(c) 0.3333
(d) 0.4444
11. Are A and B independent?
(a) Yes, P(AB)=0
(b) Yes, P(AB)=P(A)P(B)
(c) No, P(AB)0
(d) No, P(AB)P(A)P(B)
where P(AB)=0 and P(A)P(B)=(3/27)(6/27)=2/81
(e) No, P(A|B)=P(A)
Remember that being mutually exclusive does not imply the independence
12. Let’s define X as the number of cars turn left in event C, what are the possible values for x?
(a) 0
(b) 1
(c) 0,1
look at the outcomes in C and see how many cars turn left in each outcome
(d) 0,2
(e) 0,1,2
Eighty percent of all vehicles examined at a certain emissions inspection station pass the inspection. Out of all
vehicles passes the inspection, 10% have recent accident reports where out of all fails the inspection 25% have
recent accident reports. Answer the following 4 questions using this information.
13. What is the probability of the reported recent accidents?
(a) 0.05
(b) 0.08
(c) 0.13
=P(Pass inspection and accidents)+P(fail the inspection and accidents)=0.8(0.1)+0.2(0.25)
(d) 0.25
(e) 0.80
14. Given that there are recent accident reports, what is the probability that they are the vehicles failed the
inspection?
(a) 0.08
(b) 0.385
=P(accidents and fail the inspection)/P(accidents)=0.2(0.25)/[ 0.8(0.1)+0.2(0.25)]
(c) 0.572
(d) 0.615
(e) 0.92
15. If the next 2 independent vehicles are observed, what is the probability that both fail the inspection?
(a) 0.04
=P(1st vehicle fails)P(2nd vehicle fails)=0.2(0.2)
(b) 0.20
(c) 0.64
(d) 0.80
16. If the next 2 independent vehicles are observed, what is the probability that exactly one passes the inspection?
(a) 0.16
(b) 0.20
(c) 0.32
=P(1st vehicle passes)P(2nd vehicle fails)+ P(1st vehicle fails)P(2nd vehicle passes)=2(0.8)(0.2)
(d) 0.64
(e) 0.80
EXAM 1 – FORM A
STAT 211
SPRING2004
Consider the junior, sophomore and senior student classifications. There are 2 junior student workers, 5 sophomore
student workers and 3 senior student workers in a certain department. Answer the following 3 questions using this
information.
17. In how many ways can one student worker of each classification be selected for a welcoming committee?
(a) 1
(b) 5
(c) 15
(d) 30
=2(5)(3)
(e) 45
18. If two student workers are selected randomly for a welcoming committee, how many ways there are to select
them from the same classification?
(a) 10
(b) 12
(c) 14
 2 5  3 
        1  10  3
 2  2  2
= 
(d) 16
(e) 18
19. If two student workers are selected randomly for a welcoming committee, what is the probability that one will
be a junior and the other one sophomore?
(a) 0.1111
(b) 0.2222
 2  5  3  10 
   /   10 / 45
1 1  0   2 
= 
(c) 0.3333
(d) 0.4444
20. Which of the following cannot be a valid pmf (probability mass function) of X?
X
-5
0
5
10
All probabilities are between 0 and 1
Model 1: p(x) 0.30 0.20 0.20 0.30 Yes
Model 2: p(x) -0.50 0.10 0.50 0.90 No
Model 3: p(x) 0.20 0.25 0.30 0.35 Yes
(a) Only Model 1
(b) Only Model 2
(c) Only Model 3
(d) Both Model 1 and 2
(e) Both Model 2 and 3
Total probabilities
1
1
1.1