Let R denote the resistance of a resistor that is selected at random from a population of resistors that are labeled 100Ω. The true population means resistance is μR = 100 Ω, and the population standard deviation is σR = 2 Ω. 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 μE1 = μE2 = 0 and σE1 = σE2 = 10Ω. Further suppose that E1, E2, and R are independent.
a. Find σM1 and σM2.
b. Show that μM1M2 = μR2.
c. Show that μM1μM2 = μ2R.
d. Use the results of (b) and (c) to show that Cov(M1, M2) = σ2R.
e. Find ρM1,M2.