Question

Write a python program per the following specifications:

1. Populate an array(list) of size n = 50 randomly with only integers 0 and 1

2. Repeat step 1 nn = 1000 times using either a while loop or a for loop see below

At this point you should have a total of 50000 observations with either 0 or 1

This is our experimental data which we will compare to the theoretical expected result

From Lab06template.py

import random

temp = -1

n = 50

nn = 1000 # note nn*n == 50000

# Theoretical calculations

print('======Theoretical results (what is expected) ==========')

#Using the Binomial distribution formulas on page 1

p = .5

print('1 the theoretical mean(average)of 1''s ( n*nn*p)

==', temp) # fix u == n*nn*p this is the expected

(average number of 1’s

print('2 the theoretical variance v == ', temp)

# fix # v = n*nn*p*(1-p)

print('3 the standard deviation SD (should be > 100) == ', temp)

# sd = square root(v) sd = sqrt(v)

# at this point in the code # we have the theoretical mean, variance, standard deviation

# now for the experimental results

print(' ========== Experimental results ========== ')

print(' ========== Populate a list and count 1’s ========== ')

temp = -1

a = 0

b = 1

MyList = []

j = 0 while (j < nn): # loop for 1000 times

i = 0

while i < n : # loop 50 times populate list of nn

randNum = random.randint(a,b)

MyList.append(randNum)

# count the number of 1’s and the number of 0

# use the count function # the number of 1’s + number 0’s == 50

# keep track of these counts and update the results

# with the next iteration

i = i +1

j = j + 1

print('4 the length of MyList == ', temp ) # FIX

use len()

print('5 the number of 1’s is ', temp ) # FIX

print('6 the number of 0’s is ', temp ) # fix

print('7 the average of all the ', n*nn,' integers is...', 'should be < 1) ', temp) # fix

print()

# fix SD = sqrt(v)

# Display the range (+- 2sd ) as follows:

# mean+ 2*SD mean – 2*SD

print('8 mean - 2*SD == ', temp) #fix

print('9 mean + 2*SD == ', temp) #fix

# Answer the question:

# is the total number of 1’s from 5 above

# mean – 2*SD < mean < mean + 2*SD true ? Yes or no

# within the range as calculated in 8 and 9 by printing

#‘Yes’ if it is within the range and

# ‘No’ if it is not within the range

answer = 'NO'

print('10 Is the number of 1''s within ave +- 2*SD ', answer) # FIX

#Display 10 lines, 25 integers per line of the n*nn (== 50000) integers

# That is, display the integers in MyList, 25 per line, for 10 lines

# and include the line number as in 1 , 2, 3, …10

# NOTE only display 10 lines with 25 values (= 0 or 1)

# and not all 50,000 integers

print('11 displaying 10 numbered lines with 25 integers per line ...')

# for your consideration will need adjustments

k = 0

sub = []

while (k < len(MyList) ):

sub = MyList[k: k+20] # Splice

print("...",k, sub) # do NOT print k only the # line number as in 1, 2,3

k = k+2000

Answer 1

import random

import math

temp = -1

n = 50

nn = 1000 # note nn*n == 50000

# Theoretical calculations

print('======Theoretical results (what is expected) ==========')

#Using the Binomial distribution formulas on page 1

p = .5

print('1 the theoretical mean(average)of 1''s ( n*nn*p)==', n*nn*p) # fix u == n*nn*p this is the expected(average number of 1’s

print('2 the theoretical variance v == ', n*nn*p*(1-p))# fix # v = n*nn*p*(1-p)

print('3 the standard deviation SD (should be > 100) == ', math.sqrt(n*nn*p*(1-p)))

# sd = square root(v) sd = sqrt(v)

# at this point in the code # we have the theoretical mean, variance, standard deviation

# now for the experimental results

print(' ========== Experimental results ========== ')

print(' ========== Populate a list and count 1’s ========== ')

temp = 0

a = 0

b = 1

MyList = []

j = 0

while (j < nn): # loop for 1000 times

    i = 0

    while i < n : # loop 50 times populate list of nn

        randNum = random.randint(a,b)

        MyList.append(randNum)

# count the number of 1’s and the number of 0

# use the count function # the number of 1’s + number 0’s == 50

# keep track of these counts and update the results

# with the next iteration

        temp=temp+randNum

        i = i +1

    j = j + 1

print('4 the length of MyList == ', len(MyList) ) # FIX use len()

print('5 the number of 1’s is ', temp ) # FIX

print('6 the number of 0’s is ', n*nn-temp ) # fix

print('7 the average of all the ', n*nn,' integers is...', 'should be < 1) ', temp/(n*nn)) # fix

print()

# fix SD = sqrt(v)

# Display the range (+- 2sd ) as follows:

# mean+ 2*SD mean – 2*SD

print('8 mean - 2*SD == ', temp-2*(math.sqrt( (temp/(n*nn)) * (n*nn-temp)) ) ) #fix

print('9 mean + 2*SD == ', temp+2*(math.sqrt((temp/(n*nn))*(n*nn-temp)))) #fix

# Answer the question:

# is the total number of 1’s from 5 above

# mean – 2*SD < mean < mean + 2*SD true ? Yes or no

# within the range as calculated in 8 and 9 by printing

#‘Yes’ if it is within the range and

# ‘No’ if it is not within the range

answer = 'YES'

print('10 Is the number of 1''s within ave +- 2*SD ', answer) # FIX

#Display 10 lines, 25 integers per line of the n*nn (== 50000) integers

# That is, display the integers in MyList, 25 per line, for 10 lines

# and include the line number as in 1 , 2, 3, …10

# NOTE only display 10 lines with 25 values (= 0 or 1)

# and not all 50,000 integers

print('11 displaying 10 numbered lines with 25 integers per line ...')

# for your consideration will need adjustments

k = 0

sub = []

while (k < len(MyList) ):

    sub = MyList[k: k+20] # Splice

    print("...",(k/2000)+1, sub) # do NOT print k only the # line number as in 1, 2,3

    k = k+2000