I have $\displaystyle X$ is a random number uniformly distributed on $\displaystyle [0,1]$. $\displaystyle Y$ is defined to be $\displaystyle Y = -1 - \sqrt{1-X}$. I am required to find $\displaystyle E(Y)$. Here is what I have done:

We know that $\displaystyle E(X) = \int_0^1 x \ dx$. Does this imply that $\displaystyle E(Y) = E(-1 - \sqrt{1-X}) = \int_0^1 -1 - \sqrt{1-x} \ dx$?

Thank you.