degenerate bivariate normal (X,X)

From: quebecstat <quebecstat@xxxxxxx>
Date: Mon, 18 Feb 2008 07:57:06 -0800 (PST)

Let X~Normal(0,1)
Define the (degenerate) bivariate normal (X,X)
Let S={(x,y): y=x}

I would like to show that
P((X,X) is in S)=1

I am told to evaluate (for any point (a,a) in S)
P(X =< a-eps, X =<a-eps) and
P(X =< a, X =<a)
and go from there.

I really have no idea how to proceed here because the cdf and pdf do
not exist. I would much appreciate a hint.

.

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