The difference between the central limit theorems for a scalar and vector-valued random variables is
A)that n approaches infinity in the central limit theorem for scalars only.
B)the conditions on the variances.
C)that single random variables can have an expected value but vectors cannot.
D)the homoskedasticity assumption in the former but not the latter.

Question

Quizplus · Accepted Answer

The central limit theorem for scalar random variables requires that the variances of the random variables involved are finite and nonzero, while the central limit theorem for vector-valued random variables requires that the covariance matrix is positive definite.

The Difference Between the Central Limit Theorems for a Scalar