Ononot — If a distribution has a mean \mu and variance \sigma^2, and

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Central Tendencyhard

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If a distribution has a mean $\mu$ and variance $\sigma^2$ , and we define a new random variable $Y = \frac{1}{X}$ where $X > 0$ , under what condition is the Harmonic Mean $H_X$ equal to the reciprocal of the Arithmetic Mean of $Y$ ?