Answer to Question #311549 in Statistics and Probability for masedi moncho

Question

The Gaussian distribution also known as the Normal distribution, is given by the following

equation:

𝑦(𝑥) = 𝑒𝑥𝑝 −(𝑥−𝜇)^2/2𝜎^2

where parameter 𝝁 is the mean and 𝝈 the standard deviation.

(i) create a 1000 point Gaussian distribution of random numbers

having 𝜇 = 0 and 𝜎 = 1. (20)

(ii) Plot this distribution. (10)

(iii) Prove that the full width–half maximum (FWHM), of the above distribution is given by :

FWHM = 2𝜎√2ln 2 (10)

(iv) Write a program that estimates the FWHM from your data/graph. (10)

(v) Compare the theoretical and the experimental results of FWHM. (5)

(vi) What are the theoretical and experimental values of 𝒚 at FWHM?

Answer 1

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