Let R denote the resistance of a resistor that is selected at random from a population of resistors that are labeled 100 Ω. The true population mean 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 and Further suppose that E1, E2, and R are independent.

a. Find

b. Show that

c. Show that

d. Use the results of (b) and (c) to show that

e. Find

Answer :

Step 1 of 6:

Let R denote the resistance of a resistor that is selected at random from a population of resistors that are labeled

Given, the true population resistance is ,

and the population standard deviation

Let denote the measured values. Then = R + and = R + ,

Where, and are the errors in the measurements.

Suppose that, are random with and

Step 2 of 6:

a). To find

That is,

=

= 2.2361

Similarly,

=

= 2.2361

Therefore,

Step 3 of 6:

b). To show that

Then,

= (where, = R + )

=

= . (since = )

Therefore,

=

Hence proved.