Question

write code in R that does the following:

• 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 1

# Step 1: Initialize a vector for 500 numbers u=vector('numeric',500) # Step 2: Then use R to sample 5 values from U(0,5). Save the average into one of the elements of the vector. {r} s=runif(5,0,5) u[1]=mean(s) u[1] [1] 4.2477080 3.6399000 1.2084395 0.0322234 0.9072448 [1] 2.007103 # Step 3: Repeat step 2 500 times until you fill your vector. for(i in 1:500) { s=runif(5,0,5) u [i]=mean(s)

#Step 4: Take the average of your vector ave=mean (u) ave # Round your average into 4 digit **{r} C=round(ave, 4) [1] 2.4742 The averaged value is close to the $ 2.5 $ which is the actual average of uniform distribution.

The program is done in R studio.

The r Code will be

u=vector('numeric',500)

s=runif(5,0,5)
s
u[1]=mean(s)
u[1]

for(i in 1:500)
{
s=runif(5,0,5)
u[i]=mean(s)
}

ave=mean(u)
ave

c=round(ave,4)
c

If you are satisfied please rate the answer.