Problem 2 Generate 100 random samples from multivariate norm

Problem 2: Generate 100 random samples from multivariate normal distribution with mean mu = (-1, 1,6)\' and variance a . Plot all three variables pairwise. Comment on their pairwise relationship. b . Calculate the sample mean and sample variance based on your 100 samples. Also find the MLE of mean and variance matrix. c . Find the MLE of mu1 + 5sigma12.

Solution

2, 14, 24, 43, 45

9, 18, 20, 37, 47

6, 26, 39, 46, 47

4, 8, 9, 18, 21

20, 21, 26, 29, 43

7, 8, 20, 24, 37

2, 5, 30, 35, 41

29, 30, 31, 41, 47

12, 20, 38, 39, 43

24, 29, 43, 48, 50

22, 25, 26, 34, 35

7, 13, 21, 25, 33

10, 29, 33, 47, 49

4, 15, 47, 48, 50

8, 25, 29, 37, 44

13, 19, 28, 30, 40

12, 26, 27, 32, 46

2, 6, 28, 30, 50

7, 28, 29, 30, 47

10, 14, 24, 34, 40

7, 20, 37, 41, 49

11, 13, 21, 22, 27

2, 5, 7, 18, 19

1, 9, 15, 30, 45

6, 10, 31, 38, 46

8, 22, 25, 30, 37

4, 7, 12, 15, 16

10, 15, 23, 26, 49

12, 16, 25, 32, 45

23, 28, 33, 44, 49

11, 13, 15, 20, 46

27, 28, 46, 47, 49

4, 7, 8, 16, 48

1, 6, 27, 32, 45

8, 16, 19, 27, 48

4, 26, 32, 40, 46

1, 7, 27, 29, 34

9, 32, 34, 35, 43

1, 24, 28, 41, 49

7, 27, 29, 35, 47

26, 32, 35, 44, 49

17, 18, 27, 35, 39

9, 11, 32, 36, 48

6, 27, 30, 33, 34

9, 12, 24, 33, 42

2, 15, 27, 35, 38

2, 9, 21, 27, 41

5, 25, 33, 46, 47

5, 6, 28, 42, 45

17, 20, 28, 33, 46

11, 17, 22, 44, 50

3, 17, 22, 35, 39

7, 14, 16, 26, 31

10, 21, 33, 42, 49

14, 33, 34, 37, 41

16, 18, 20, 23, 38

4, 8, 15, 22, 49

3, 12, 30, 39, 45

21, 32, 34, 39, 46

Set #1: 2, 14, 24, 43, 45