Perfectly correlated random variables

I have a set of identically distributed Weibull's (or pick any other dist.) and they are all perfectly correlated. Can I treat them as a single Weibull with the same parameters as as a single Weibull, in order to determine moments and probabilities?

-

In some cases of uncorrelated but dependent random variables, one might not need all the variables. For example, if $X$ is a random variable with symmetric density (that is, $f_X(x) = f_X(-x)$) and with finite third moment, then $X$ and $Y = X^2$ are uncorrelated random variables, but we don't need $Y$ if we have $X$. –  Dilip Sarwate Oct 26 '12 at 4:28