Use Rstudio code. Please show the code in R studio(R) and
screenshot it. Thank you！
Use Rstudio Code Please Show The Code In R Studio R And Screenshot It Thank You 1 (96.63 KiB) Viewed 36 times
Problem 3 (R - 19 points). You have learned in probability that the sampling distribution of Xn is not normally distributed when X; * N (1,0). However, Central Limit Theorem tells us that the distribution should converge to a normal distribution in the limit as n, the sample size, grows to infinity. In this problem, you will investigate this visually, and by comparing probabilities calculated from CLT and from simulation. Parts (a)- (b) require plotting, but all other parts can be completed independently without these graphs. The Weibull distribution is defined by two parameters: shape (a > 0) and scale (B > 0) and has the following density function: Q-1 а f(xla, 3) = ; (?). | e-(x/B)", > 0 Weibull distributed random variables have the following expected value and variance: E(X) = B. 1(1+1/a) V(X) = B2. (I (1 + 2/a) – (1(1+1/a))?) - [(y) is the Gamma function, and can be tricky to compute if y is not a positive integer. Instead, you can calculate the values using R using the gamma(y) function. See ?gamma for usage information.
e) (2 points) Repeat (f) for sample size n = 120. How does the normal approximation compare with the simulated probability now? f) (4 point) Which of the two computed probabilities (normal approximation versus simulation) is more accurate to the true probability? Briefly explain why it is more accurate. How can the normally approximated probability be made more accurate? How can the simulated probability be more accurate? BONUS (2 points) Upload separately in Crowdmark. Reproduce your graph from (b) using grid.arrange, this time with each histogram overlaid with the normal density curve you would use when applying CLT for those sample sizes. With the overlay, can you better determine which sample size results in a sample mean that has an approximately normal distribution?
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