M.Phil Physics
Course: Computational Physics (Stochastic Methods)
Home Work # 3
This assignment is based on Random Sampling of pdfs
Due date: One Week after this distribution in class.
Question 1
(a) Suppose that a given pdf for y is shown below:
10)2exp(4)( 2<<−= yyyyf
Then first normalize this pdf and then using Direct sampling method find out
a proper formula to sample this distribution.
(b) Use MATLAB program and sample the pdf for N = 10000. Draw both the
exact and sampled distribution functions as histograms.
(c) What happens when N is increased to 100000? Show results as graphs
and give some sort of comparison.
Question 2
(a) For above pdf use rejection method and sample randomly for N = 10000.
Draw both the exact and sampled distribution function.
(a) Find out the efficiency of this technique. What happens when N is
increased to 100000? Show results as graphs and give some sort of
comparison.
Question 3
(b) For above pdf use Metropolis Algorithm and sample randomly for N =
10000. Draw both the exact and sampled distribution function.
(c) Find out the efficiency of this technique. What happens when N is
increased to 100000? Show results as graphs and give some sort of
comparison.
Home Work # 3
1
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