6) Multivariate Normal Distribution

Question 1

What is the mean vector and covariance matrix

Answer 1

Question 2

What are the properties of expectation and covariance for a random vector

Answer 2

Question 3

How does the covariance formula for a transformed random vector generalise the variance formula for random variables

Answer 3

Question 4

When is a matrix symmetric and a positive semidefinite

Answer 4

Question 5

What are the properties of the covariance matrices

Answer 5

• symmetric
• Positive semidefinite

Question 6

What is a factor of Σ

Answer 6

Question 7

What is a a standard multivariate normal distribution

Answer 7

Question 8

What is a multivariate normal distribution

Answer 8

Question 9

What are the expectation and covariance of a multivariate normal random vector

Answer 9

Question 10

What is the mgf of a random vector

Answer 10

Question 11

What is the mgf of a multivariate normal random vector

Answer 11

Question 12

How is the distribution of a random vector defined if it is a linear combination

Answer 12

Question 13

When are the components of a multivariate normal random vectorindependent

Answer 13

Question 14

Answer 14

Question 15

What is the p.d.f. of a multivariate normal random vector Z∼N(0,I)

Answer 15