Question

I need help with part g. Use R

• step 1. initialize a vector for 500 numbers. • step 2. Then use R to sample 5 values from U(0,5), a uniform distribution with min=0 and max=5. Save the average of these uniform numbers into one of the elements of this vector. • Repeat step 2 500 times in a loop until you've filled up your vector. • Finally, take the average of your vector (the average of the 500 averages)! What number did you get? Please report this number to the nearest four digits. This will help you check that your code is right. Answer: 2.4856 Part 1: Uniform Distribution & the Central Limit Theorem g) Also in your Jupyter Notebook, add one more line of code to do the following: • Using the same vector of length 500 that you used in part f), take the variance of your vector. What number did you get? Please report this number to the nearest four digits. Answer: 0.1245 Check

Answer 1

x= rep(NA, 500)

for ( i in (1 : 2500)){
y <- runif(5,0,5)
x[i] = mean(y)
}

mean(x)
var(x)

mean(x) [1] 2.51055 var (x [1] 0. 3984814

here variance = 0.3985

you may want to use set.seed so that answer is fixed