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# Use trigonometry or calculus to find same area AssignmentTutorOnline | Good Grade Guarantee!

Distinguish between an exact replication and a conceptual replication. What is the value of a conceptual replication?
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Let f (x) = (sin x)2 for 0 < x=””>< 2π.=””>(a) Graph the function.
(b) Use Monte Carlo integration to find the area under f (x) on the range 0 < x=””>< 2π,=”” and=”” to=”” find=”” a=”” 95%=”” confidence=”” interval=”” for=”” the=”” area.=””>
(c) Use trigonometry or calculus to find the same area exactly. Did the confidence interval cover the true value?
(d) Write a function called rsin2 which generates random values from the density f (x)/k, 0 < x=””>< 2π,=”” where=”” k=”” is=”” the=”” area=”” found=”” above.=”” the=”” function=”” should=”” take=”” a=”” single=”” argument=”” specifying=”” how=”” many=”” samples=”” are=”” required,=”” e.g.=”” rsin2(10)=”” would=”” return=”” a=”” vector=”” of=”” 10=”” samples=”” from=”” this=”” distribution.=”” use=”” the=”” rejection=”” method=”” to=”” draw=”” the=”” samples.=”” plot=”” a=”” histogram=”” based=”” on=”” 1000=”” samples.=””>
(e) Use your function to draw a sample of 1 000 000 samples, and calculate a 95% confidence interval for the mean. (By symmetry, the true mean must be π. Did your confidence interval cover the true value?) 