So I have a question from statistical inference that I need some help with:
$X_1,X_2,...,X_5$ are jointly multivariate normal with means = $\mu_i$, variances = $\sigma^2_i$, correlation = $\rho$
Among the many parts of this question, I am asked: "What is the marginal distribution of $X_2$? Cite a result to support your statement"
Is this a one-line, verbal response?? Is this a calculation? I don't quite know how to approach this. If anyone had any advice, or guidance that you were willing to share I'd be grateful. Thanks.
This is a one-liner. The marginal distributions of a multivariate normal are normal with the associated mean and variance of that variable. Note: the converse is not true, as others may point out.