Let $X$ be a standard Gaussian random variable. Is the $\mathbb R^2$-valued random variable $(X,X)$ absolutely continuous ?
I don't understand the question here. Now $X$ has density $\frac{1}{2\pi}\exp(-\frac{x^2}{2})$
I have to find out if the cumulative distribution function is continuous right ?, but how is cdf defined in more dimensional case ?
Does it have to do something with Radon-Nikodym theorem, marginal distributions ?