Reference no: EM131029160
Central Limit Theorem Exercise
Write a computer program or Excel spreadsheet that:
a. takes a given distribution function (f(x), as given below), for x between: 0 and 1.0,
b. randomly samples this function at n points and determines the mean for that sample
c. repeats b. N times
d. plots a histogram of the result of the above c. with a (suggested) bin resolution of 0.2.
e. and plots the original distribution function on the same plot as above in d.
f. use this for cases A-C below.
A. Use f(x) = 1.0 for N = 10,000 and n=2, n=4, n=8, and n=32.
B. Use f(x) = x for n = 2 and n= 32.
C. Use f(x) = - x2 + 1 for n=2, n=4, n=8, and n=32.
D. For n = 32 in A, B, and C, plot the results (without the distribution function) overplotting a Gaussian determined by estimating the amplitude and width by eye for the histogram of the result. Do the histograms seem to be Gaussian?
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