Question

From successive sums of 12 uniform random variables (i.e., use the BASIC system RND() function) use the Central Limit Theorem and BASIC to generate a long sequence (>1000) of Normal random variables with zero mean and unity variance. Calculate the mean and variance for N=10,000 observations.

Answer 1

just want to understand the general idea of what the teach is asking

Answer 2

so basically create 1000 normal random variables using z = RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() -6

Answer 3

add them all up and find the average

Answer 4

from this, calculate the variance? why is it that you have 1000 pieces of sample data and 10,000 observations???

Answer 5

im in this class too
i did something like this
08 N=10000
09 for J = 1 to N
10 for I = 1 to 12
11 x = 0
20 X = X + rnd(1)
30 next I
40 SUM = SUM + X - 6
41 AVG = SUM / N
50 print sum
60 print N
70 print AVG

Answer 6

hey sorry was looking at a another page

Answer 7

thats not right though

Answer 8

wait so you just do this for 10,000 numbers?

Answer 9

why does he have >1000

Answer 10

greater than 1000 is 10000

Answer 11

its unclear

Answer 12

yeah, not sure why he wrote it that way

Answer 13

are you in the 1pm class?

Answer 14

yes

Answer 15

ahh nice, i usually sit towards the back

Answer 16

grr this assignment is killing me. usually have everything done way ahead of schedule but had a bunch of other stuff due, so i'm struggling with finishing this last minute

Answer 17

how did you set up problem 2?

Answer 18

im in the same boat. although i'm a lifelong procrastinator.

Answer 19

lol

Answer 20

on your program i think you have it set up right except for lines 11 - 30

Answer 21

you should do RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() + RND() - 6

Answer 22

set that = to X

Answer 23

im testing it now, definite logic error

Answer 24

ah wait nm, you had it right. but yeh just add 10000 of them up then divide

Answer 25

import java.util.*;
import java.lang.Math;

public class NormalRNDVars {


public static void main(String[] args) {
Random rand = new Random();
double rnd = rand.nextDouble();
double z[] = new double[1002];
double average = 0, sum = 0, sample = 0;

//Calculate normal random variable
for(int i=1; i<=1000; i++) {
z[i] = rnd + rnd + rnd + rnd + rnd + rnd + rnd + rnd + rnd + rnd + rnd + rnd - 6;
}

//Add all of the normal random variables
for(int i=1; i<=1000; i++) {
sum += z[i];
}

//Calculate and print the average
average = sum / 10000;
System.out.printf("Average: %f\n", average);

for(int i=1; i<=1000; i++) {
sample += Math.pow(z[i] - average, 2);
}

sample = sample / (1000 - 1);

System.out.printf("Variance: %f\n", sample);


}

}

Answer 26

if that helps

Answer 27

gotta catch a bus, cya in class

Answer 28

bye