# Math Help - Continuous distribution expectation

1. ## Continuous distribution expectation

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

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

Thank you.

2. ## Re: Continuous distribution expectation

Hey Diadem.

Your are close but not quite correct. Recall that E[a + bX] = a + b*E[X] for constants a and b. This implies

E[-1 - SQRT(1-X)] = -1 - E[SQRT(1-X)] = -1 - Integral [0,1] sqrt(1-x)*1*dx.