Cybersecurity The table below lists the frequency of leading digits of Internet traffic interarrival times for a computer, along with the percentages of each leading digit expected with Benford’s law.

c. Use the results from part (b) to find the contribution to the x2 test statistic from the category representing the leading digit of 2.

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with calculating the contribution to the chi-squared (χ²) test statistic for the category representing the leading digit of 2. The χ² test statistic measures the difference between observed and expected frequencies.

Step 2: Identify the observed frequency (O) for the leading digit of 2. From the table, the observed frequency is 62.

Step 3: Calculate the expected frequency (E) for the leading digit of 2. Use the percentage from Benford's Law (17.6%) and multiply it by the total number of observations. To find the total number of observations, sum all the observed frequencies in the table.

Step 4: Use the formula for the contribution to the χ² test statistic for the leading digit of 2: χ²_contribution = ((O - E)^2) / E. Substitute the observed frequency (O) and the expected frequency (E) into the formula.

Step 5: Simplify the expression to find the contribution to the χ² test statistic for the leading digit of 2. This value will be part of the overall χ² test statistic.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Benford's Law

Benford's Law predicts the frequency distribution of leading digits in many real-life sets of numerical data. According to this law, smaller digits occur as the leading digit more frequently than larger digits. For example, the digit '1' appears as the leading digit about 30.1% of the time, while '9' appears only about 4.6% of the time. This phenomenon is often used in fraud detection and data analysis.

Chi-Squared Test

The Chi-Squared test is a statistical method used to determine if there is a significant difference between the expected and observed frequencies in categorical data. In this context, it helps assess how well the observed leading digits of interarrival traffic times fit the expected frequencies according to Benford's Law. The test statistic is calculated by summing the squared differences between observed and expected values, divided by the expected values.

Contribution to Chi-Squared Statistic

The contribution to the Chi-Squared statistic for a specific category is calculated by taking the squared difference between the observed frequency and the expected frequency for that category, divided by the expected frequency. This contribution helps identify which categories deviate most from what is expected under Benford's Law, providing insight into the data's distribution and potential anomalies.