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Let R be the actual resistance of a resistor that is selected at random from a batch of 100 N' resistors produced by a certain factory. The '100 N’ resistors produced by the factory are of course not exactly 100 N each. They are actually random with mean uR deviation ơR Now, let's suppose that the resistance of our randomly selected reistor from this batch is measured twice with an ohmmeter. Let M¡ and M2 denote the measured values. Then M1 = R+Ej and M, = R+ E2, where E, and E, are the measurement errors. Suppose further that E¡ and E, are random with means zero and standard deviations 1 N. Assuming that R, E1, and E2 are mutually independent, = 100 N and standard 2 Ω. %3D %3D %3D a) find the standard deviations of M¡ and M2, b) show that the expected value of M, M2 is just equal to the expected value of R2, c) show also that E [M¡]E [M2] = E² [R].

Let R be the actual resistance of a resistor that is selected at random from a batch of 100 N' resistors produced by a certain factory. The '100 N’ resistors produced by the factory are of course not exactly 100 N each. They are actually random with mean uR deviation ơR Now, let's suppose that the resistance of our randomly selected reistor from this batch is measured twice with an ohmmeter. Let M¡ and M2 denote the measured values. Then M1 = R+Ej and M, = R+ E2, where E, and E, are the measurement errors. Suppose further that E¡ and E, are random with means zero and standard deviations 1 N. Assuming that R, E1, and E2 are mutually independent, = 100 N and standard 2 Ω. %3D %3D %3D a) find the standard deviations of M¡ and M2, b) show that the expected value of M, M2 is just equal to the expected value of R2, c) show also that E [M¡]E [M2] = E² [R].

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let R be the actual resistance of a resistor that is selected at random from a batch of '100 N' resistors produced by a certain factory. The 100 N' resistors produced by the factory are of course not exactly 100 N each. They are actually random with mean uR = 100 N and standard deviation oR Now, let's suppose that the resistance of our randomly selected reistor from this batch is measured twice with an ohmmeter. Let M and M, denote the measured values. Then = R+E, and M, = R+ E2, where E, and E, are the measurement errors. Suppose further = 2 N. M that E, and E, are random with means zero and standard deviations 1 N. Assuming that R, E1, and E2 are mutually independent, 6. a) find the standard deviations of M and M2, b) show that the expected value of M1 M, is just equal to the expected value of R2, c) show also that E [M¡] E [M2] = E² [R]. d) use the results of (b) and (c) to show that Cov M1, M2 = on, e) find the correlation coefficient between Mj and M2.
Transcribed Image Text:Let R be the actual resistance of a resistor that is selected at random from a batch of '100 N' resistors produced by a certain factory. The 100 N' resistors produced by the factory are of course not exactly 100 N each. They are actually random with mean uR = 100 N and standard deviation oR Now, let's suppose that the resistance of our randomly selected reistor from this batch is measured twice with an ohmmeter. Let M and M, denote the measured values. Then = R+E, and M, = R+ E2, where E, and E, are the measurement errors. Suppose further = 2 N. M that E, and E, are random with means zero and standard deviations 1 N. Assuming that R, E1, and E2 are mutually independent, 6. a) find the standard deviations of M and M2, b) show that the expected value of M1 M, is just equal to the expected value of R2, c) show also that E [M¡] E [M2] = E² [R]. d) use the results of (b) and (c) to show that Cov M1, M2 = on, e) find the correlation coefficient between Mj and M2.
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