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Answer :
Final answer:
The random variable 'X' is the number of suspicious transactions to be reviewed until finding the first that needs to be blocked. Given the characteristics of this situation, 'X' follows a Geometric distribution, which describes the number of attempts before a first success in situations where each attempt is independent and has two outcomes.
Explanation:
The random variable of interest in this question, which we can define as 'X', would be the number of suspicious transactions the specialist needs to review until reaching the first transaction that will be blocked. Given the nature of the question, where we're concerned with the number of attempts until the first success, the random variable 'X' is best described by a Geometric distribution.
In a Geometric distribution, we are interested in the number of Bernoulli trials needed to get the first success. Here, a 'success' would be encountering a transaction that needs to be blocked which implies it is suspicious. The trials (reviews of transactions) are independent, meaning the outcome of one does not affect the others, and each trial has only two possible outcomes - 'success' or 'failure' (the transaction needs to be blocked or it doesn't).
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Rewritten by : Barada
The expected value of blocked transactions by the specialist is 54.4. The random variable of interest is the number of reviews until the first block is found which follows a geometric distribution.
a) The expected value refers to a generalization of the weighted average. In an experiment with number of n trails and probability of success on a single trail p, the expected value of blocked transaction is given by:
E(X) = np where n is the number of trails and p is the probability of transaction block is 0.4.
Hence,
E(X) = 136*0.4 = 54.4
b) The random variable of interest be the random variable X represents the number of reviews until the first block is found. X follows a geometric distribution as it is used to model the first transaction.
Note: The question is incomplete. The complete question probably is: 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. (b) Suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked. Define the random variable of interest and state how the variable is distributed.
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