Chapter 4: Multivariate Distribution

Question 1

When is the variance of a t-distributed random variable defined and what does it equal?

Answer 1

When k > 2 it is defined and equal to k / (k - 2).

Question 2

When is the expectation of a t-distributed random variable defined and what does it equal?

Answer 2

When k > 2 it is defined and equal to zero.

Question 3

Describe the relationship between marginal and joint normal distributions.

Answer 3

Two jointly normal distributed random variables will be marginal normal too. However, two marginal normal distributions need not be jointly normal

Question 4

Give the definition of a t-distributed random variable - both in terms of a standardized expression and in terms of a variable already standardized.

Question 5

Calculate S_pooled for the two-sample t-test (univariate case).

Answer 5

(n1-1)S1^2+(n2-1)S2^2 / n1+n2-2.