I have is a random number uniformly distributed on . is defined to be . I am required to find . Here is what I have done:
We know that . Does this imply that ?
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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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