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Let R denote the resistance of a resistor that is selected at random from a population of resistors that are labeled 100?. The true population means resistance is ?R = 100 ?, and the population standard deviation is ?R = 2 ?. The resistance is measured twice with an ohmmeter. Let M1 and M2 denote the measured values.

Then M1 = R + E1 and M2 = R + E2, where E1 and E2 are the errors in the measurements. Suppose that E1 and E2 are random with ?E1 = ?E2 = 0 and ?E1 = ?E2 = 10?. Further suppose that E1, E2, and R are independent.

a. Find ?M1 and ?M2.

b. Show that ?M1M2 = ?R2.

c. Show that ?M1?M2 = ?2R.

d. Use the results of (b) and (c) to show that Cov(M1, M2) = ?2R.

e. Find ?M1,M2.

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