Transcript Lecture 15

UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
2 summands
UNR, MATH/STAT 352, Spring 2007
3 summands
UNR, MATH/STAT 352, Spring 2007
4 summands
UNR, MATH/STAT 352, Spring 2007
5 summands
UNR, MATH/STAT 352, Spring 2007
6 summands
UNR, MATH/STAT 352, Spring 2007
7 summands
UNR, MATH/STAT 352, Spring 2007
8 summands
UNR, MATH/STAT 352, Spring 2007
9 summands
UNR, MATH/STAT 352, Spring 2007
10 summands
UNR, MATH/STAT 352, Spring 2007
20 summands
UNR, MATH/STAT 352, Spring 2007
30 summands
UNR, MATH/STAT 352, Spring 2007
40 summands
UNR, MATH/STAT 352, Spring 2007
50 summands
UNR, MATH/STAT 352, Spring 2007
100 summands
UNR, MATH/STAT 352, Spring 2007
1000 summands
UNR, MATH/STAT 352, Spring 2007
UNR, MATH/STAT 352, Spring 2007
Consider Normal random variable
X with mean 5 and variance 1
UNR, MATH/STAT 352, Spring 2007
Normal Probability Plot for 10 observations
99
ML Estimates
95
90
Percent
80
70
60
50
40
30
20
10
5
1
3.5
4.5
5.5
6.5
Data
UNR, MATH/STAT 352, Spring 2007
7.5
Mean:
5.54806
StDev:
0.632073
Normal Probability Plot for 50 observations
99
ML Estimates
95
90
Percent
80
70
60
50
40
30
20
10
5
1
2
3
4
5
6
Data
UNR, MATH/STAT 352, Spring 2007
7
8
Mean:
4.90914
StDev:
1.10260
Normal Probability Plot for 500 observations
ML Estimates
99
Percent
95
90
80
70
60
50
40
30
20
10
5
1
2
3
4
5
6
Data
UNR, MATH/STAT 352, Spring 2007
7
8
Mean:
4.97043
StDev:
0.967118
Consider Normal random variable
X with mean 5 and variance 1,
consider now Y = X2
UNR, MATH/STAT 352, Spring 2007
Normal Probability Plot for 10 observations
99
ML Estimates
95
90
Percent
80
70
60
50
40
30
20
10
5
1
5
15
25
35
45
Data
UNR, MATH/STAT 352, Spring 2007
55
Mean:
31.1804
StDev:
7.71668
Normal Probability Plot for 50 observations
99
ML Estimates
95
90
Percent
80
70
60
50
40
30
20
10
5
1
0
10
20
30
Data
40
50
Mean:
25.3154
StDev:
11.0370
Normal Probability Plot for 500 observations
ML Estimates
99
Percent
95
90
80
70
60
50
40
30
20
10
5
1
0
20
40
Data
60
Mean:
25.6405
StDev:
9.75542
Consider Normal random variable
X with mean 5 and variance 1,
consider now Y = (X-5)2
UNR, MATH/STAT 352, Spring 2007
Normal Probability Plot for 10 observations
99
ML Estimates
95
90
Percent
80
70
60
50
40
30
20
10
5
1
-4
-3
-2
-1
0
1
2
3
Data
UNR, MATH/STAT 352, Spring 2007
4
5
6
Mean:
0.699882
StDev:
1.45573
Normal Probability Plot for 50 observations
99
ML Estimates
95
90
Percent
80
70
60
50
40
30
20
10
5
1
-3
-2
-1
0
1
2
3
4
Data
UNR, MATH/STAT 352, Spring 2007
5
6
7
Mean:
1.22399
StDev:
1.67449
Normal Probability Plot for 500 observations
ML Estimates
99
Percent
95
90
80
70
60
50
40
30
20
10
5
1
0
5
Data
UNR, MATH/STAT 352, Spring 2007
10
Mean:
0.936192
StDev:
1.30413