True or false:

a. A covariance matrix is singular if and only if it is positive definite.

b. A covariance matrix is nonsingular if and only if it is positive semidefinite.

c. Every random vector has a positive semidefinite covariance matrix.

a. False: A positive definite covariance matrix is never singular.

b. False: A positive semi-definite covariance matrix may be singular.

c. False: If second moments for a random vector don't exist, it won't even have a covariance matrix.