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Fraudulent numbers in tax returns, payment records, invoices, etc. often display patterns that aren’t present in...

Fraudulent 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 probability distribution, where the random variable x is the first digit of the number. x 1 2 3 4 5 6 7 8 9 P(x) 0.301 0.176 0.125 ? 0.079 0.067 0.058 0.051 0.046 (a) Find the probability that the first digit is a 4. (b) Let A be the event that the first digit is a 1 or a 2; B be the event that the first digit is more than 6 and C be the event that the first digit is an odd number. Find P(A), P(B) and P(C). (c) Find the probabilities for the following events i. P(A and B) ii. P(A or B) iii. P(A and B) iv. P(B|C) (d) Based on your result from part (i.) above, what can you say about the relationship between events A and B? (e) Find the mean and standard deviation for the probability distribution.

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