If the mean of $x$ and $1/x$ is $M$, then the mean of $... – Statistics

Statisticshard · Past Paper

If the mean of $x$ and $1/x$ is $M$, then the mean of $x^2$ and $1/x^2$ is:

A$M^2$

B$2M^2 - 1$

C$2M^2 + 1$

D$4M^2 - 1$

✓ Correct Answer: B — $2M^2 - 1$

$(x+1/x)/2 = M \Rightarrow x+1/x = 2M. Squaring: x^2 + 1/x^2 + 2 = 4M^2 \Rightarrow x^2 + 1/x^2 = 4M^2 - 2. Mean = (4M^2-2)/2 = 2M^2-1$.

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