Open the Excel file GSB 519 Additional Years of Life for Males. The random variable x =.5, 1.5, 2.5,…..,110.5, where x denotes additional years of life beyond age zero. The second column shows the probability that each specific value of x occurs. This column contains the probability mass values, f(x). For example, the probability that a new-born male baby will live 20.5 years (not less or not more) is .00133349, i.e., f(20.5) = .00133349. Find the following properties of the random variable x. a. mean b. median c. mode d. variance e. standard deviation f. skewness g. kurtosis h. coefficient of variation i. Find the value of the distribution function F(x) when x = 65.5. j. How much total probability is contained within two standard deviations of the mean? [You should use Excel in order to avoid hand calculations. However, do not use Excel commands like AVERAGE or STDEV; you will get incorrect answers if you do.] Addition Years of Life Probability of Additional Years Beyond Age Zero of Life Beyond Age Zero x f(x) 0.5 0.00751 1.5 0.00056 2.5 0.00038 3.5 0.00029 4.5 0.00024 5.5 0.00019 6.5 0.00017 7.5 0.00015 8.5 0.00016 9.5 0.00016 10.5 0.00018 11.5 0.00018 12.5 0.0002 13.5 0.00025 14.5 0.00032 15.5 0.000460073 16.5 0.000685573 17.5 0.000917926 18.5 0.001199153 19.5 0.00135626 20.5 0.00133349 21.5 0.001472586 22.5 0.001402542 23.5 0.001352221 24.5 0.001358685 25.5 0.001282876 26.5 0.001347743 27.5 0.001297042 28.5 0.001358564 29.5 0.001318775 30.5 0.001378847 31.5 0.001359142 32.5 0.001408642 33.5 0.001545099 34.5 0.001634408 35.5 0.001793465 36.5 0.001830896 37.5 0.002058594 38.5 0.002218989 39.5 0.002318003 40.5 0.002497214 41.5 0.002625624 42.5 0.002829616 43.5 0.003127286 44.5 0.003371848 45.5 0.00363289 46.5 0.003865731 47.5 0.004286488 48.5 0.004594853 49.5 0.004860601 50.5 0.005204666 51.5 0.005403102 52.5 0.005796129 53.5 0.005999806 54.5 0.006883906 55.5 0.006782889 56.5 0.007789865 57.5 0.008396484 58.5 0.009423117 59.5 0.009462798 60.5 0.010712697 61.5 0.011239357 62.5 0.012274465 63.5 0.013113627 64.5 0.014132136 65.5 0.015179913 66.5 0.015977036 67.5 0.017252954 68.5 0.018356019 69.5 0.01954698 70.5 0.020510339 71.5 0.021720101 72.5 0.023166495 73.5 0.024551701 74.5 0.025450939 75.5 0.026803467 76.5 0.02780352 77.5 0.028734712 78.5 0.029889624 79.5 0.030836513 80.5 0.030723819 81.5 0.032875337 82.5 0.031112913 83.5 0.032654009 84.5 0.032164248 85.5 0.031555646 86.5 0.030541532 87.5 0.029139249 88.5 0.027383883 89.5 0.025327342 90.5 0.023035959 91.5 0.020586718 92.5 0.018062365 93.5 0.015545866 94.5 0.013114783 95.5 0.010836205 96.5 0.008762786 97.5 0.006930345 98.5 0.00535721 99.5 0.004045269 100.5 0.003527413 101.5 0.002 102.5 0.002 103.5 0.001 104.5 0.0005 105.5 0.0002 106.5 0.00015 107.5 0.00008 108.5 0.00004 109.5 0.00002 110.5 0.00001

Open the Excel file GSB 519 Additional Years of Life for Males. The random variable x =.5, 1.5, 2.5,…..,110.5, where x denotes additional years of life beyond age zero. The second column shows the probability that each specific value of x occurs. This column contains the probability mass values, f(x). For example, the probability that a new-born male baby will live 20.5 years (not less or not more) is .00133349, i.e., f(20.5) = .00133349. Find the following properties of the random variable x. a. mean b. median c. mode d. variance e. standard deviation f. skewness g. kurtosis h. coefficient of variation i. Find the value of the distribution function F(x) when x = 65.5. j. How much total probability is contained within two standard deviations of the mean? [You should use Excel in order to avoid hand calculations. However, do not use Excel commands like AVERAGE or STDEV; you will get incorrect answers if you do.] Addition Years of Life Probability of Additional Years Beyond Age Zero of Life Beyond Age Zero x f(x) 0.5 0.00751 1.5 0.00056 2.5 0.00038 3.5 0.00029 4.5 0.00024 5.5 0.00019 6.5 0.00017 7.5 0.00015 8.5 0.00016 9.5 0.00016 10.5 0.00018 11.5 0.00018 12.5 0.0002 13.5 0.00025 14.5 0.00032 15.5 0.000460073 16.5 0.000685573 17.5 0.000917926 18.5 0.001199153 19.5 0.00135626 20.5 0.00133349 21.5 0.001472586 22.5 0.001402542 23.5 0.001352221 24.5 0.001358685 25.5 0.001282876 26.5 0.001347743 27.5 0.001297042 28.5 0.001358564 29.5 0.001318775 30.5 0.001378847 31.5 0.001359142 32.5 0.001408642 33.5 0.001545099 34.5 0.001634408 35.5 0.001793465 36.5 0.001830896 37.5 0.002058594 38.5 0.002218989 39.5 0.002318003 40.5 0.002497214 41.5 0.002625624 42.5 0.002829616 43.5 0.003127286 44.5 0.003371848 45.5 0.00363289 46.5 0.003865731 47.5 0.004286488 48.5 0.004594853 49.5 0.004860601 50.5 0.005204666 51.5 0.005403102 52.5 0.005796129 53.5 0.005999806 54.5 0.006883906 55.5 0.006782889 56.5 0.007789865 57.5 0.008396484 58.5 0.009423117 59.5 0.009462798 60.5 0.010712697 61.5 0.011239357 62.5 0.012274465 63.5 0.013113627 64.5 0.014132136 65.5 0.015179913 66.5 0.015977036 67.5 0.017252954 68.5 0.018356019 69.5 0.01954698 70.5 0.020510339 71.5 0.021720101 72.5 0.023166495 73.5 0.024551701 74.5 0.025450939 75.5 0.026803467 76.5 0.02780352 77.5 0.028734712 78.5 0.029889624 79.5 0.030836513 80.5 0.030723819 81.5 0.032875337 82.5 0.031112913 83.5 0.032654009 84.5 0.032164248 85.5 0.031555646 86.5 0.030541532 87.5 0.029139249 88.5 0.027383883 89.5 0.025327342 90.5 0.023035959 91.5 0.020586718 92.5 0.018062365 93.5 0.015545866 94.5 0.013114783 95.5 0.010836205 96.5 0.008762786 97.5 0.006930345 98.5 0.00535721 99.5 0.004045269 100.5 0.003527413 101.5 0.002 102.5 0.002 103.5 0.001 104.5 0.0005 105.5 0.0002 106.5 0.00015 107.5 0.00008 108.5 0.00004 109.5 0.00002 110.5 0.00001

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

a. mean

b. median

c. mode

d. variance

e. standard deviation

f. skewness

g. kurtosis

h. coefficient of variation

i. Find the value of the distribution function F(x) when x = 65.5.

j. How much total probability is contained within two standard deviations of the mean?

[You should use Excel in order to avoid hand calculations. However, do not use Excel commands like AVERAGE or STDEV; you will get incorrect answers if you do.]

Addition Years of Life	Probability of Additional Years
Beyond Age Zero	of Life Beyond Age Zero
x	f(x)
0.5	0.00751
1.5	0.00056
2.5	0.00038
3.5	0.00029
4.5	0.00024
5.5	0.00019
6.5	0.00017
7.5	0.00015
8.5	0.00016
9.5	0.00016
10.5	0.00018
11.5	0.00018
12.5	0.0002
13.5	0.00025
14.5	0.00032
15.5	0.000460073
16.5	0.000685573
17.5	0.000917926
18.5	0.001199153
19.5	0.00135626
20.5	0.00133349
21.5	0.001472586
22.5	0.001402542
23.5	0.001352221
24.5	0.001358685
25.5	0.001282876
26.5	0.001347743
27.5	0.001297042
28.5	0.001358564
29.5	0.001318775
30.5	0.001378847
31.5	0.001359142
32.5	0.001408642
33.5	0.001545099
34.5	0.001634408
35.5	0.001793465
36.5	0.001830896
37.5	0.002058594
38.5	0.002218989
39.5	0.002318003
40.5	0.002497214
41.5	0.002625624
42.5	0.002829616
43.5	0.003127286
44.5	0.003371848
45.5	0.00363289
46.5	0.003865731
47.5	0.004286488
48.5	0.004594853
49.5	0.004860601
50.5	0.005204666
51.5	0.005403102
52.5	0.005796129
53.5	0.005999806
54.5	0.006883906
55.5	0.006782889
56.5	0.007789865
57.5	0.008396484
58.5	0.009423117
59.5	0.009462798
60.5	0.010712697
61.5	0.011239357
62.5	0.012274465
63.5	0.013113627
64.5	0.014132136
65.5	0.015179913
66.5	0.015977036
67.5	0.017252954
68.5	0.018356019
69.5	0.01954698
70.5	0.020510339
71.5	0.021720101
72.5	0.023166495
73.5	0.024551701
74.5	0.025450939
75.5	0.026803467
76.5	0.02780352
77.5	0.028734712
78.5	0.029889624
79.5	0.030836513
80.5	0.030723819
81.5	0.032875337
82.5	0.031112913
83.5	0.032654009
84.5	0.032164248
85.5	0.031555646
86.5	0.030541532
87.5	0.029139249
88.5	0.027383883
89.5	0.025327342
90.5	0.023035959
91.5	0.020586718
92.5	0.018062365
93.5	0.015545866
94.5	0.013114783
95.5	0.010836205
96.5	0.008762786
97.5	0.006930345
98.5	0.00535721
99.5	0.004045269
100.5	0.003527413
101.5	0.002
102.5	0.002
103.5	0.001
104.5	0.0005
105.5	0.0002
106.5	0.00015
107.5	0.00008
108.5	0.00004
109.5	0.00002
110.5	0.00001

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

Expert Solution

Step 1

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The mean formula is as follows.

$E (X) = \sum_{i = 1}^{n} x_{i} P (X = x_{i})$

$n$ is the sample size.

The median is as follows.

$M = \frac{m + n}{2}$

$m$ is the largest value of $X$ such that

$P (X \leq m) \leq 0.5$

$n$ is the smallest value of $X$ such that

$P (X \leq m) \geq 0.5$

The mode is the value of $X$ for which the probability mass function is maximized.

The given data is as follows.

The random variable $X$ is additional years of life beyond age zero

$x_{i}$	$P (X = x_{i})$
0.5	0.00751
1.5	0.00056
2.5	0.00038
3.5	0.00029
4.5	0.00024
5.5	0.00019
6.5	0.00017
7.5	0.00015
8.5	0.00016
9.5	0.00016
10.5	0.00018
11.5	0.00018
12.5	0.00020
13.5	0.00025
14.5	0.00032
15.5	0.00046
16.5	0.00069
17.5	0.00092
18.5	0.00120
19.5	0.00136
20.5	0.00133
21.5	0.00147
22.5	0.00140
23.5	0.00135
24.5	0.00136
25.5	0.00128
26.5	0.00135
27.5	0.00130
28.5	0.00136
29.5	0.00132
30.5	0.00138
31.5	0.00136
32.5	0.00141
33.5	0.00155
34.5	0.00163
35.5	0.00179
36.5	0.00183
37.5	0.00206
38.5	0.00222
39.5	0.00232
40.5	0.00250
41.5	0.00263
42.5	0.00283
43.5	0.00313
44.5	0.00337
45.5	0.00363
46.5	0.00387
47.5	0.00429
48.5	0.00459
49.5	0.00486
50.5	0.00520
51.5	0.00540
52.5	0.00580
53.5	0.00600
54.5	0.00688
55.5	0.00678
56.5	0.00779
57.5	0.00840
58.5	0.00942
59.5	0.00946
60.5	0.01071
61.5	0.01124
62.5	0.01227
63.5	0.01311
64.5	0.01413
65.5	0.01518
66.5	0.01598
67.5	0.01725
68.5	0.01836
69.5	0.01955
70.5	0.02051
71.5	0.02172
72.5	0.02317
73.5	0.02455
74.5	0.02545
75.5	0.02680
76.5	0.02780
77.5	0.02873
78.5	0.02989
79.5	0.03084
80.5	0.03072
81.5	0.03288
82.5	0.03111
83.5	0.03265
84.5	0.03216
85.5	0.03156
86.5	0.03054
87.5	0.02914
88.5	0.02738
89.5	0.02533
90.5	0.02304
91.5	0.02059
92.5	0.01806
93.5	0.01555
94.5	0.01311
95.5	0.01084
96.5	0.00876
97.5	0.00693
98.5	0.00536
99.5	0.00405
100.5	0.00353
101.5	0.00200
102.5	0.00200
103.5	0.00100
104.5	0.00050
105.5	0.00020
106.5	0.00015
107.5	0.00008
108.5	0.00004
109.5	0.00002
110.5	0.00001

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