Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions. (a) Suppose the specialist will review 136 suspicious transactions in one day. What is the expected number of blocked transactions by the specialist? Show your work.

To find the expected number of blocked transactions, we can use the formula for expected value in probability. The expected number of blocked transactions can be calculated as: \[ E(X) = n \times p \] where: - \( n \) is the total number of transactions reviewed, - \( p \) is the probability of a transaction being blocked. In this case, we have: - \( n = 136 \) (the number of suspicious transactions) - \( p = 0.40 \) (the probability of blocking a transaction) Substituting these values into the formula gives us: \[ E(X) = 136 \times 0.40 \] Calculating that: \[ E(X) = 54.4 \] So, the expected number of blocked transactions is approximately **54.4**. Since we can't block a fraction of a transaction, we can say that on average, the specialist would block about **54 transactions**. Now, let’s summarize our work: 1. Identified the total number of transactions (\(n\)). 2. Used the blocking probability (\(p\)). 3. Applied the expected value formula. 4. Calculated to find the expected number of blocked transactions. Therefore, we expect roughly 54 transactions to be blocked based on the specialist’s review.