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I'm looking for solving this problem to find the closed form solution if it is possible:

[itex]Y=\frac{1}{X}[/itex]

Where X is uniform random variable > 0

I know the expected value for X which is [itex]\overline{X}[/itex]

is there a method to find the expected value of Y which is [itex]\overline{Y}[/itex] in term of [itex]\overline{X}[/itex] as closed form solution?

I know how to calculate it easily using numerical solution, but I need it for modeling problem and I need the analytical solution.

Thanks

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# The inverse of uniform random variable

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