Problem 12E

The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (θ, θ + 1), where θ is the true but unknown voltage of the circuit. Suppose that Y1, Y2, . . . , Yn denote a random sample of such readings.

a Show that is a biased estimator of θ and compute the bias.

b Find a function of that is an unbiased estimator of θ .

c Find is used as an estimator of θ .

Section 1 Fund. Facts of Circuit Theory Definitions o Electricity characteristic of the universe that may be used to transmit energy and to transmit information o Charge electric charge is a characteristic of electrons and protons Protons positive charge Electrons negative charge Neutrons no charge o Voltagea measure of the work required to more 1 coulomb of charge btwn 2 points (nodes) in a network o Current measure of time rate of flow of electrical charge through a circuit element Current is through a circuit o Power the time rate at which energy is dissipated in a circuit element o Resistance the volta