MATH t/group/7able152-bd26-4feb-8ec7-faacaa9f34cc/Written%20Assignments/Written%20Assignr m Ontario Security Gu... B Brock University -... B Brock Sakai : Home... G Grammarly 3 / 3 - 80% + STAT/MATH 1F92 Assignment 2 2021-2022 c) Find the probability for each event. Show your work. not B ii. A or B iii. A and B What is the relationship between these events? d) Suppose you receive 1,000 invoices from a company that is under investigation. You are asked to provide evidence as to the legitimacy of the records. We simulate the first digits of these 1,000 invoices on Excel with the following steps. Click on cell A1 > Click on the function icon fx. Choose the "Math & Trig" category. Select "RANDBETWEEN" function and click OK. Enter "1" for "Bottom" and enter "9" for "Top" and click OK. After getting the random number in the first cell, highlight that cell, scroll down 1,000 cells, hold the "Shift" button and then click the 1,000th cell. The column should now be highlighted. Underneath the "Home" tab click "Fill - Down" ( ]. ). All entries should now be filled with random numbers. Obtain a histogram of the first digits for the 1,000 invoices. Use upper class limits of 1.5, 2.5, ..., 9.5. On your chart and histogram, rename the labels for each class to be 1, 2, ..., 9. Submit a screenshot of the chart and histogram. Ensure the title and axis labels are descriptive. e) Refer to the chart output from d). Obtain empirical probabilities for P(A), P(B), and P(C) using relative frequency approximations. Show your work. f) Compare your empirical probabilities in e) to the theoretical probabilities in b). Is there any evidence to suggest the invoices are not legitimate? Explain. O X Omodel. 2. Faked numbers in tax returns, payment records, invoices, etc. often display patterns that aren't present in legitimate records. It is a striking fact that the first digits of numbers in legitimate records often have probabilities that follow the model (known as Benford's Law) partially shown in the following table. First Digit 2 3 4 5 6 7 8 9 Probability ? 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 a) Find the probability that the first digit is a 1. Show your work. b) Define the following events A = the first digit is a 2 or a 3 B = the first digit is more than 6 C = the first digit is an even number Find P(A), P(B), and P(C). Show your work. 2