This problem involves using R to examine the Central Limit Theorem more in detail. For all answers in this problem, round to four decimal places. We will first generate 10 Poisson(}l=1) random variables and then calculate the sample mean of these 10 random variables. We will do this process 10,000 times to generate 10,000 simulated sample means. Run the following code and use the output to answer the following questions. set.seed(2020) nsims 10000 # number of simulations means rep(0,nsims) # vector to store sample mean from each simulation for(i in 1:nsims){ data = rpois(n=10,lambda=1) means[i] = mean(data) } hist(means) mean(means) sd(means) (a) What is the sample mean of the 10,000 simulations? 0.99302 (b) From theory, what is E[)_(] for this example? (This is a hand calculation not using R.) (c) What is the standard deviation of the 10,000 simulations? (d) From theory, what is SE[)_(] for this example? (This is a hand calculation not using R.) (e) What proportion of the simulated sample means are less than 0.9? (If you don't remember how to do this operation in R, look back at your previous homework assignments.) (f) Using the Central Limit Theorem, calculate the (approximate) probability that P()_(