Statisticshard · Past Paper
If the mean of x and 1/x is M, what is the mean of x^2 and 1/x^2?
AM^2
B2M^2 - 1
CM^2 - 2
D4M^2 - 2
✓ Correct Answer: B — 2M^2 - 1
(x + 1/x)/2 = M => x + 1/x = 2M. Squaring gives x^2 + 2 + 1/x^2 = 4M^2 => x^2 + 1/x^2 = 4M^2 - 2. Mean = (4M^2 - 2) / 2 = 2M^2 - 1.
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