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Math Help - Continuous distribution expectation

  1. #1
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    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.
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  2. #2
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    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.
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