AppliedMultiple choice

For a positive random variable $X$ that is not constant, how do $\mathbb{E}[1/X]$ and $1/\mathbb{E}[X]$ compare?

A $\mathbb{E}[1/X] > 1/\mathbb{E}[X]$
B $\mathbb{E}[1/X] < 1/\mathbb{E}[X]$
CThey are equal
DIt depends on the distribution of $X$

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Linearity of expectation

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For a positive random variable XXX that is not constant, how do E[1/X]\mathbb{E}[1/X]E[1/X] and 1/E[X]1/\mathbb{E}[X]1/E[X] compare?

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For a positive random variable $X$ that is not constant, how do $\mathbb{E}[1/X]$ and $1/\mathbb{E}[X]$ compare?