[R] statistics/correlation question NOT R question

[Leeds, Mark (IED)]

This is not an R question but if anyone can help me, it's much
appreciated.

Suppose I have a series ( stationary ) y_t and a series x_t ( stationary
)and x_t has variance sigma^2_x and epsilon is normal 
(0, sigma^2_epsilon )

and the two series have the relation

					y_t = Beta*x_t + epsilon

My question is if there are particular values that sigma^2_x and
sigma^2_epsilon have to take in order for corr(x_t,y_t) to equal Beta ?

I attempted to figure this out using two different methods and in one
case I end up involving sigma^2_epsilon and in the other I don't
and I'm not sure if either method is correct. I think I need to use
results form the conditional bivariate normal but i'm really not sure.
Also, it's not a homework problem because I am too old to have homework.
Thanks for any insights/solutions.
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