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A random variable $X$ has the density function

$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$

(b) Compute $\text{E(1/X)}$.
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I am getting c = 6/7 and Harmonic Mean, E(1/X) = 18/7