Q1. The radius of a circle is measured with an error of measurement, which is N(0, σ^2). Let x1, x2, ..., xn be n measurements of the radius. Let \barx = (∑i=1n xi)/(n) be the sample mean and S2 = (∑i=1n (xi - \barx)^2)/(n-1) be the sample variance. What is the unbiased estimate of the area of the circle?
- (a) π(\barx)2
- (b) π (∑i=1n xi^2)/(n)
- (c) π \(∑i=1n xi^2)/(n) - S2\
- (d) π \{(\barx)2 - S2\}