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 oR = 2 N. 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+E, and M2 = R+E2, where E, and E2 are the measurement errors. Suppose further that E and E2 are random with means zero and standard deviations 1 N. Assuming that R, E1, and E, are mutually independent, = 100 N and standard a) find the standard deviations of M1 and M2, b) show that the expected value of M1M2 is just equal to the expected value of R², c) show also that E [M¡] E [M2] = E² [R]. %3| d) use the results of (b) and (c) to show that Cov [M1, M2 = oR, e) find the correlation coefficient between M1 and M2.
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 oR = 2 N. 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+E, and M2 = R+E2, where E, and E2 are the measurement errors. Suppose further that E and E2 are random with means zero and standard deviations 1 N. Assuming that R, E1, and E, are mutually independent, = 100 N and standard a) find the standard deviations of M1 and M2, b) show that the expected value of M1M2 is just equal to the expected value of R², c) show also that E [M¡] E [M2] = E² [R]. %3| d) use the results of (b) and (c) to show that Cov [M1, M2 = oR, e) find the correlation coefficient between M1 and M2.
MATLAB: An Introduction with Applications
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only d and e please
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ea15aad-ce09-44c1-ae1a-fd69c581a5af%2Fc9e7808a-e44e-4542-b4ab-c5c37c619d6e%2Fek2i01_processed.png&w=3840&q=75)
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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