# (d)Write a function called rsin2 which generates random values from the density f(x)/k, 0

(d)Write a function called rsin2 which generates random values from the density f(x)/k, 0 < x < 211 , 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 i. Did your confidence interval cover the true value?) v <- runif (10000, min=0,max = 2*pi) mean(sin(v)^2)*((2*pi)-0) p<-rep (0,1000) for(i in 1:1000){ set.seed(1) N<-runif (1000, min=0,max=2*pi) p[i]<-((2pi)/999) *sum((sin(n))^2) } psort<-sort (p) psort [25] #Lower bound of 95% confidence interval psort [975] Hupper bound of 95% confidence interval [1] 3.168996 [1] 3.000482 [1] 3.280129

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