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Albany College of Pharmacy Uniform Distribution Question

Albany College of Pharmacy Uniform Distribution Question

Question Description

NOTE: Please read the bottom of “Getting Started with R” regarding its use in HW problems, suchas 1.5/4 below. Answer questions in all parts, especially those involving the output, and indicate!4. ? In this problem, we will gain some more fundamental practice with the Rprogramming language. Some of the terms and concepts may appear unfamiliar, but wewill formally define them later. For now, just use basic intuition.[R Tip: At the prompt (>), repeatedly pressing the “up arrow” ? on your keyboard willstep through your previous commands in reverse order.](a) First, consider a “uniformly distributed” (i.e., evenly scattered) population of agesbetween 0 and 100 years. What is the mean age of this population? (Use intuition.)Let us simulate such a population, by generating an arbitrarily large (say one million)vector of random numbers between 0 and 100 years. Type, or copy and pastepopulation = runif(1000000, 0, 100)at the prompt (>) in the R console, and hit Enter.Let us now select a single random sample of n = 500 values from this population viarand = sample(population, 500)then sort them from lowest to highest, and round them to two decimal places:my.sample = round(sort(rand), 2)Type my.sample to view the sample you just generated. (You do not need to turn this in.)(b) Compute the mean age of my.sample. How does it compare with the mean found in (a)?(c) The R command hist graphs a “frequency histogram” of your data. Moreover,?hist gives many options under Usage for this command. As an example, graph:hist(my.sample, breaks = 5, xlab = “Ages”, border = “blue”,labels = T)Include and interpret the resulting graph. Does it reasonably reflect the uniformlydistributed population? Explain.(d) Repeat (b) and (c) several more times using different samples of n = 500 data values.How do these sample mean ages compare with the population mean age in (a)?(e) Suppose many random samples of size n = 500 values are averaged, as in (d). Graph theirhistogram via the R code below, and offer a reasonable explanation for the resulting shape.vec.means = NULLfor (i in 1:2000){vec.means[i] = mean(sample(population, 500))}hist(vec.means, xlab = “Mean Ages”, border = “darkgreen”)

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