Question

Python, given a code in class i just need help with the third bullet point ; using a and n (defined in the second picture of python code) find the first digit for k! for k =1,...,n. you dont have to type in all this code just help me write the code in the first picture where it says: def benford(a):

b = [0 for d in range(1,10)]

#Do everthything in here

return b

2.2 Generating data In this assignment you will generate data using your factorial function. In particular, you will: Let the number n denote the number of data points to generate. Conorate k' for k = 1, , n. Call this sequence (ai, , an), where ak- . Using (ai, , an), find the first digit in k! for k-1, , n. Call this sequence (bi, ,bn), where bk įs the first digit of k!. . Using (bi, . . . ,h), tally the data to get the counts sequence (c, . . . ,c), where cd İs the number of occurrences of the digit d in the sequence b. Naturally, c9 Using (c. ..,co), normalize the tally by the number of data points to get the empirical fraction (fi. where fa-ca/n is the fraction of integers k for which the first digit of k! is d. ,fo) » Use matplotlib to create a pair of bar plots comparing the empirical data (fi,... , /o) with the prediction from Benford's Law (p,... ,Po) 1 from math import log16e 2 from math import log10, floor 3 import numpy as np 4import matplotlib.pyplot as plt 6# ECE 105: Programming for Engineers II (Spring, 2019) 7# Lab 2) Problem 2) Part 1 8# April 11-12, 2019 9# PLEASE rename this solution .py file as your "username-2.ру" (e.g. spW26-2.py 11# generate the sequenc k k! 12 def factSeq (n): return [np.math.factorial(k) for k in range(1,n+1)] 13 14 # given any array (a1, ,an), return (f1, ,f9) 15% where fd is the fraction of numbers in array with first digit d 16 def benford (a): 17 # TODO Return the correct array (fl, ,f9) 18 b [e for d in range(1,10 19 #do everything in here 20 21 return b e of factorials (al,...,an) where a 23 24# aggregate relative error between f and p 25 def error(f,p): 26 return sum(Cabs (f[d] -p[d])/p[d] for d in range(9)]) # PLEASE DO NOT CHANGE THE CODE BELOW ! n = 1000 # sequence Length def main) import sys import re try: student-id = sys . argv [0]. split('/') [-1] student_id = re . match(' ([a-z]+\d+)*-2", if not student_id: student-id) print("PLEASE CHANGE YOUR FILE NAME !") student id "None" except: student id "None" a = factSeq(n) # factorials (a1, ,an) with ak = k! f = benford(a) # empirical data (f1, f9), fd is fraction starting with d p = [log10(1+1/d) for d in range(1,10)] # Benford's Law prediction (p1, ,p e benTable(f,p) # print the results in a text table

Answer 1

Below is the complete code for your benford() function, it returns the normalised data.

import numpy as np def fact (n): return [np.math.factorial(k) for k in range (1,n+1)] def benford (a): b-[e for d in range (1,10)] for num in a: # Traverse each element in array num- str(num) # Convert number first to string first int(num[0]) # Extract first digit by indexing b[first-1] +-1 # incre se the count in b, accessing by index # You can check your b list by printing below line #print("count of first digit",b, "Sum of elemnts in b ",sum(b)) # Below line is the alternative to perform element wise division np.array(b)/ten(a) # Loop to perform noramlisation for i in range(len (b)) b[i]b[i]/len(a) return b x fact (18) print("Factorials-",x) print("Normalised -",benford(x)) Factorials[1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800] Normalised [e.2, 0.2, 6.2, 0.1, 0.1, 0.1, 0.1, 0.0, .e]