You plan to use a rod to lay out a square, each side of which is the length of the rod. The length of the rod is μ, which is unknown. You are interested in estimating the area of the square, which is μ^2. Because μ is unknown, you measure it n times, obtaining observations X1, X2,..., Xn. Suppose that each measurement is unbiased for μ with variance σ^2. a. Is X^2 a biased or an unbiased estimate of the area of the square? b. Find an unbiased estimate of the area of the square.
1. You plan to use a rod to lay out a square, each side of which is the length of the rod.
The length of the rod is μ, which is unknown. You are interested in estimating the area
of the square, which is μ^2. Because μ is unknown, you measure it n times, obtaining
observations X1, X2,..., Xn. Suppose that each measurement is unbiased for μ with
variance σ^2.
a. Is X^2 a biased or an unbiased estimate of the area of the square?
b. Find an unbiased estimate of the area of the square.
Given Information:
A rod is used to lay out a square, each side of the square is the length of the rod.
The length of the rod is μ.
The area of the square is to be estimated.
μ is unknown, you measure it n times, obtaining observations .
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