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If a probability density function is fx(x) = 5x^4 for 0<x<1 and 0 elsewhere, then the expected value of E[x^0.5] is the integral of ∫x^0.5*fx(x) between 0 and 1 which is 10/11.
However if I try to approach it as the expected value of Y=X^0.5 then I find fy(y) = 5*lny/y^4 and its expected value is 20/33.
What's wrong? Is it a right approach or are those two things different?
However if I try to approach it as the expected value of Y=X^0.5 then I find fy(y) = 5*lny/y^4 and its expected value is 20/33.
What's wrong? Is it a right approach or are those two things different?