Benford's Law looks at the distribution of first digits of naturally occurring numbers. This can apply to populations, heights of random mountains, and even business record numbers. The distribution can be used, for example, to detect fraudulent records by noticing when certain digits appear too oftenl Here is the distribution in table form, where X is the first digit of a randomly chosen value. "mm-E- Probabillt But why isn't the same probability for every number? There are many ways to explain it mathematically, but the simplest explanation is that numbers that start with a 1 come before the other numbers. Suppose that we have some set of records with a last number of 4,237. A random record starting with a 1, 2, or 3 will be more likely than the other numbers. And no matter what record we stop at, the 1'5 will always be included in the list of most likely first digits! Questions: Use the distribution in the table above to answer the following questions: (Note that you do no; need to use the data you recorded.) 1) If we add all the values in the second row of the table, what do we get? Why does this make sense? 2] What is P(X = 7)? 3) What is P(X = 7 orX = B)? 4) What is P(X > 7)? 5) What is P(X = 1)? 6) What is P(X 2 6)? 7) Which of the previous two probabilities is larger? In your own words, explain what this says about the first digits of random records. 8) If three records are chosen at random, what is the probability that they all start with the digit 1? 9) If three records are chosen at random, what is the probability that none starts with the digit 1