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b) In the muon lifetime experiment, we obtain a histogram for the recorded decays as function of the time after the muon enters the detector. After binning the decays into discrete time bins, we expect the distribution of decays (histogram) to be described by an exponential function of time. Rather than fitting the data directly with an exponential function, it is sometimes more convenient to plot the logarithm of the decays in a bin (y;) as a function of time (x₁) and then fit a straight line to it. Each data point of the histogram (x, y) has a statistical error, 0₁ = √√₁, associated with it. What happens to these errors when the semi-log histogram 12 11

b) In the muon lifetime experiment, we obtain a histogram for the recorded decays as function of the time after the muon enters the detector. After binning the decays into discrete time bins, we expect the distribution of decays (histogram) to be described by an exponential function of time. Rather than fitting the data directly with an exponential function, it is sometimes more convenient to plot the logarithm of the decays in a bin (y;) as a function of time (x₁) and then fit a straight line to it. Each data point of the histogram (x, y) has a statistical error, 0₁ = √√₁, associated with it. What happens to these errors when the semi-log histogram 12 11

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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b) In the muon lifetime experiment, we obtain a histogram for the recorded decays as function of the time after the muon enters the detector. After binning the decays into discrete time bins, we expect the distribution of decays (histogram) to be described by an exponential function of time. Rather than fitting the data directly with an exponential function, it is sometimes more convenient to plot the logarithm of the decays in a bin (y;) as a function of time (x₁) and then fit a straight line to it. Each data point of the histogram (x, y) has a statistical error, 0₁ = √√, associated with it. What happens to these errors when the semi-log histogram (x, log10 y.) is plotted? Assume that all values of y, are >> 1. = c) In a separate experiment, you find that log10 Eo 1.5±0.5 (at 68% confidence level, CL). What is the value of E, and the experimental bounds at 68% CL? (Note that 0.5 is not small compared to 1.5).
Transcribed Image Text:b) In the muon lifetime experiment, we obtain a histogram for the recorded decays as function of the time after the muon enters the detector. After binning the decays into discrete time bins, we expect the distribution of decays (histogram) to be described by an exponential function of time. Rather than fitting the data directly with an exponential function, it is sometimes more convenient to plot the logarithm of the decays in a bin (y;) as a function of time (x₁) and then fit a straight line to it. Each data point of the histogram (x, y) has a statistical error, 0₁ = √√, associated with it. What happens to these errors when the semi-log histogram (x, log10 y.) is plotted? Assume that all values of y, are >> 1. = c) In a separate experiment, you find that log10 Eo 1.5±0.5 (at 68% confidence level, CL). What is the value of E, and the experimental bounds at 68% CL? (Note that 0.5 is not small compared to 1.5).
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Hello! As you have posted 2 different questions, we are answering the first question. In case you require the unanswered question also, kindly re-post them as separate question.

b)

In the given situation, a histogram is recorded decays as function of the time after the muon enters the detector.

That is, the decays is defined as yi and the time as xi.

Each data point of the histogram xi,yi has a statistical error, σi=yi, associated with it.

 

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