Two independent experiments measure the theory parameter y. The negative log-likelihood as a function of the parameter y is given by: Experiment 1: -InL = 0.6 + 1.2(x - 1.6) 2 Experiment 2: -InL = 0.5+ 1.8(x - 1.4)2 a) For each experiment, calculate the central value and the value of the negative In at the central value. b) For each experiment, calculate the (1-0) uncertainty on the central value and state the final result in the format x = xxxx. c) Use the two -In curves to find the average of the two experiments and its standard deviation. d) A third, independent, experiment measures a value pf x3 = 1.3 + -0.5. Determine the average of the three experiments and its standard derivation.
Two independent experiments measure the theory parameter y. The negative log-likelihood as a function of the parameter y is given by: Experiment 1: -InL = 0.6 + 1.2(x - 1.6) 2 Experiment 2: -InL = 0.5+ 1.8(x - 1.4)2 a) For each experiment, calculate the central value and the value of the negative In at the central value. b) For each experiment, calculate the (1-0) uncertainty on the central value and state the final result in the format x = xxxx. c) Use the two -In curves to find the average of the two experiments and its standard deviation. d) A third, independent, experiment measures a value pf x3 = 1.3 + -0.5. Determine the average of the three experiments and its standard derivation.
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Transcribed Image Text:Two independent experiments measure the theory parameter y. The negative log-likelihood as
a function of the parameter y is given by:
Experiment 1: -InL = 0.6 + 1.2(x - 1.6) 2
Experiment 2: -InL = 0.5+ 1.8(x - 1.4)2
a) For each experiment, calculate the central value and the value of the negative In at the
central value.
b) For each experiment, calculate the (1-0) uncertainty on the central value and state the final
result in the format x = xxxx.
c) Use the two -In curves to find the average of the two experiments and its standard
deviation.
d)
A third, independent, experiment measures a value pf x3 = 1.3 + -0.5. Determine the
average of the three experiments and its standard derivation.
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