Please do the attached question (explained please) thanks (d)electromagnetic waves. An engineer wants to check if both instruments are calibrated identically, i.e., if they will produceidentical measurements for identical waves. To do so, the engineer does nį independent measurements of the intensity ofthe a given wave using the first instrument, and n2 measurements on the same wave using the second instrument. Theintegers n1 and n2 may not be equal because, for instance, one instrument may be more costly than the other one, or mayproduce measurements more slowly. The measurements are denoted by {X;}"1, for the first instrument and by {Y;}"2,for the second one. Intrinsic defects of the instruments will lead to measurement errors, and it is reasonable to assumethat {X;}""1 are iid Gaussian and so are {Y;}",²1. If the two instruments are identically calibrated, {X;}""1 and {Y;}";²1should have the same expectation but may not have the same variance, since the two instruments may not have the sameprecision. Hence, we assume that X; ~ N (µ1, 0ỉ) and Y; ~ N (µ2,0), where µ1, H2 E R and of, osamples are independent of each other. We want to test whether µ1 = µ2. Let pû1, pû2, o²,o be the maximum likelihoodestimators of µ1; µ2; 07,0% respectively.Comparing two means: Consider two measuring instruments that are used to measure the intensity of somei=1ISj=1Si=1> 0, and that the twon202?What is the distribution ofofLet A = ûj – û2. What is the distribution of A?

Name: Please do the attached question (explained please) thanks (d)electroma
Uploaded: 2024-03-20T07:06:27.000Z
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Description: Please do the attached question (explained please) thanks (d)electromagnetic waves. An engineer wants to check if both instruments are calibrated identically, i.e., if they will produceidentical measurements for identical waves. To do so, the enginee

X and Y are iid random variables with n1 and n2 size .

Math

Statistics

al measurements for identical waves. To do so, the engineer de iven wave using the first instrument, and n2 measurements c sni and n2 may not be equal because, for instance, one instru e measurements more slowly. The measurements are denoted second one. Intrinsic defects of the instruments will lead to X;}"', are iid Gaussian and so are {Y;}"21. If the two instrum have the same expectation but may not have the same varian on. Hence, we assume that X; ~ N (u1,o?) and Y, ~N (u2,o: