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{"ops":[{"insert":"The Gaussian distribution also known as the Normal distribution, is given by the following "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"equation: "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":" \ud835\udc66(\ud835\udc65) = \ud835\udc52\ud835\udc65\ud835\udc5d \u2212(\ud835\udc65\u2212\ud835\udf07)^2\/2\ud835\udf0e^2"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"where parameter \ud835\udf41 is the mean and \ud835\udf48 the standard deviation. "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(i) create a 1000 point Gaussian distribution of random numbers"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"having \ud835\udf07 = 0 and \ud835\udf0e = 1. (20)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(ii) Plot this distribution. (10)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(iii) Prove that the full width\u2013half maximum (FWHM), of the above distribution is given by : "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":" FWHM = 2\ud835\udf0e\u221a2ln 2 (10)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(iv) Write a program that estimates the FWHM from your data\/graph. (10)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(v) Compare the theoretical and the experimental results of FWHM. (5)"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"(vi) What are the theoretical and experimental values of \ud835\udc9a at FWHM? "},{"insert":"\n"}]}

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