8.12 The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (0, +1), where 0 is the true but unknown voltage of the circuit. Suppose that Y₁, Y2,..., Y, denote a random sample of such readings. a Show that Y is a biased estimator of and compute the bias. b Find a function of Y that is an unbiased estimator of 0. C Find MSE(Y) when Y is used as an estimator of 0.
8.12 The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (0, +1), where 0 is the true but unknown voltage of the circuit. Suppose that Y₁, Y2,..., Y, denote a random sample of such readings. a Show that Y is a biased estimator of and compute the bias. b Find a function of Y that is an unbiased estimator of 0. C Find MSE(Y) when Y is used as an estimator of 0.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:8.12
The reading on a voltage meter connected to a test circuit is uniformly distributed over the
interval (0, +1), where 0 is the true but unknown voltage of the circuit. Suppose that
Y₁, Y2,..., Y, denote a random sample of such readings.
a Show that Y is a biased estimator of and compute the bias.
b Find a function of Y that is an unbiased estimator of 0.
C
Find MSE(Y) when Y is used as an estimator of 0.
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