Quiz

The multivariate normal distribution is the most important mathematical tool we need in this course. This quiz gives you the opportunity to check if you have understood the main properties of the multivariate normal distribution as used in this course.

Question 1

Which of the following properties of the multivariate normal distribution are true? Multiple answers are possible.

It is symmetric around the mean.

It is multimodal.

It is completely described by its mean and variance.

Its conditional distribution is again a normal distribution.

The marginal distribution is a chi-squared distribution..

Question 2

The multivariate normal distribution models...

…a single random variable.

…a vector of random variables (i.e. a random vector).

…a matrix of random variables (i.e. a random matrix).

…a function of random variables (i.e. a random function).

Question 3

What do the diagonal entries in the covariance matrix represent?

The variance of each component of the random vector.

The standard deviation of each component of the random vector.

The correlation between two components of the random vector.

Question 4

What properties do we require from a covariance matrix to hold? Multiple answers are possible.

It should be symmetric.

It should be orthogonal.

It should be positive definite (or at least semi-definite).

Question 5

What can we say about the conditional distribution of a multivariate normal distribution? Multiple answers are possible.

It is again a normal distribution.

It can be computed efficiently.

We have an analytic solution for the mean and covariance matrix.

Question 6

What can we say about the marginal distribution of a multivariate normal distribution? Multiple answers are possible.

It is again a normal distribution.

It can be computed efficiently.

We have an analytic solution for the mean and covariance matrix.