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Two unknowns, two moments for a normal fit

You model the size of a bid-ask spread (in ticks) as a normal distribution with unknown mean μ\mu and unknown variance σ2\sigma^2. From a large sample you compute the average 1nXi=2\frac{1}{n}\sum X_i = 2 and the average of the squares 1nXi2=13\frac{1}{n}\sum X_i^2 = 13.

Use the method of moments to estimate μ\mu and σ2\sigma^2.

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