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# Univariate Distribution Test Problems Variance Template 1 2 3 ixif(xi) xif(xi) xif(xi) xif(xi) 919130.01 30.01 40.02 20.11 928260.12 60.12 50.24 30.13 937370.24 70.24 60.1...

Univariate Distribution
Test Problems
Variance Template                            1            2            3
i    xi    f(xi)                        xi    f(xi)        xi    f(xi)        xi    f(xi)
91    9    1    3    0.01                        3    0.01        4    0.02        2    0.11
92    8    2    6    0.12                        6    0.12        5    0.24        3    0.13
93    7    3    7    0.24                        7    0.24        6    0.1        5    0.12
94    6    4    8    0.1                        8    0.1        9    0.08        8    0.07
95    5    5    10    0.03                        10    0.03        12    0.08        10    0.07
96    4    6    11    0.06                        11    0.06        15    0.08        12    0.02
97    3    7    14    0.15                        14    0.15        17    0.07        14    0.05
98    2    8    16    0.02                        16    0.02        20    0.15        17    0.26
99    1    9    18    0.14                        18    0.14        21    0.04        18    0.07
100    0    10    21    0.13                        21    0.13        23    0.14        20    0.1
Weighted Average            Variance                Var    29.38        Var    48.59        Var    43.6
Standard Deviation                St Dev    5.42        St Dev    6.97        St Dev    6.6
Bivariate Distribution
Source Data                                            Variance Template                            Test Problems
Max Prob    Space Left    Formula            y                i    xi    f(xi)                    1            y
1    92    8    0.24            1    2    3        1                                        1    2    3
2    93    7    0.12    x    1    0.04    0.04    0.10        2                                x    1    0.04    0.04    0.10
3    94    6    0.07        2    0.30    0.09    0.07        3                                    2    0.30    0.09    0.07
4    95    5    0.02        3    0.09    0.04    0.23            Weighted Avg            Var(x)                    3    0.09    0.04    0.23
5    96    4    0.15                                            Standard Deviation                            Var(x)    0.51
6    97    3    0.05                                                                        Var(y)    0.83
7    98    2    0.07    Covariance(x+y)                        i    yi    f(yi)                                    Var(s)    1.51
8    99    1    0.13                            1                                            Variance(x+y)    0.09
9    100    0    0.15                            2
3                            2            y
Weighted Avg            Var(y)                        1    2    3
Standard Deviation                x    1    0.24    0.08    0.14
2    0.15    0.02    0.02
i    si    f(si)                            3    0.05    0.09    0.21
1                                            Var(x)    0.80
2                                            Var(y)    0.81
3                                            Var(s)    2.11
4                                            Variance(x+y)    0.25
5
Weighted Avg            Var(s)            3            y
Standard Deviation                        1    2    3
x    1    0.21    0.08    0.02
2    0.15    0.18    0.12
3    0.01    0.04    0.19
Var(x)    0.55
Var(y)    0.70
Var(s)    1.98
Variance(x+y)    0.37

## Solution

Pooja answered on Mar 15 2022
Univariate Distribution
Test Problems
Variance Template                            1            2            3
i    xi    f(xi)                        xi    f(xi)        xi    f(xi)        xi    f(xi)
91    9    1    3    0.01    -8.86    78.50    0.78            3    0.01        4    0.02        2    0.11
92    8    2    6    0.12    -5.86    34.34    4.12            6    0.12        5    0.24        3    0.13
93    7    3    7    0.24    -4.86    23.62    5.67            7    0.24        6    0.1        5    0.12
94    6    4    8    0.1    -3.86    14.90    1.49            8    0.1        9    0.08        8    0.07
95    5    5    10    0.03    -1.86    3.46    0.10            10    0.03        12    0.08        10    0.07
96    4    6    11    0.06    -0.86    0.74    0.04            11    0.06        15    0.08        12    0.02
97    3    7    14    0.15    2.14    4.58    0.69            14    0.15        17    0.07        14    0.05
98    2    8    16    0.02    4.14    17.14    0.34            16    0.02        20    0.15        17    0.26
99    1    9    18    0.14    6.14    37.70    5.28            18    0.14        21    0.04        18    0.07
100    0    10    21    0.13    9.14    83.54    10.86            21    0.13        23    0.14        20    0.1
Weighted Average    11.86        Variance    29.38            Var    29.38        Var    48.59        Var    43.6
Standard Deviation    5.42            St Dev    5.42        St Dev    6.97        St Dev    6.6
1)
Variance Template
i    xi    f(xi)
1    3    0.01    -8.86    78.50    0.78
2    6    0.12    -5.86    34.34    4.12
3    7    0.24    -4.86    23.62    5.67
4    8    0.1    -3.86    14.90    1.49
5    10    0.03    -1.86    3.46    0.10
6    11    0.06    -0.86    0.74    0.04
7    14    0.15    2.14    4.58    0.69
8    16    0.02    4.14    17.14    0.34
9    18    0.14    6.14    37.70    5.28
10    21    0.13    9.14    83.54    10.86
Weighted Average    11.86        Variance    29.38
Standard Deviation    5.42
2)
Variance Template
i    xi    f(xi)
1    4    0.02    -9.01    81.18    1.62
2    5    0.24    -8.01    64.16    15.40
3    6    0.1    -7.01    49.14    4.91
4    9    0.08    -4.01    16.08    1.29
5    12    0.08    -1.01    1.02    0.08
6    15    0.08    1.99    3.96    0.32
7    17    0.07    3.99    15.92    1.11
8    20    0.15    6.99    48.86    7.33
9    21    0.04    7.99    63.84    2.55
10    23    0.14    9.99    99.80    13.97
Weighted Average    13.01        Variance    48.59
Standard Deviation    6.97
3)
Variance Template
i    xi    f(xi)
1    2    0.11    -9.09    82.63    9.09
2    3    0.13    -8.09    65.45    8.51
3    5    0.12    -6.09    37.09    4.45
4    8    0.07    -3.09    9.55    0.67
5    10    0.07    -1.09    1.19    0.08
6    12    0.02    0.91    0.83    0.02
7    14    0.05    2.91    8.47    0.42
8    17    0.26    5.91    34.93    9.08
9    18    0.07    6.91    47.75    3.34
10    20    0.1    8.91    79.39    7.94
Weighted Average    11.09        Variance    43.60
Standard Deviation    6.60
BD_p1
Source Data                                            Variance Template                            Test Problems
Max Prob    Space...
SOLUTION.PDF