(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. (i) Define the random variable of interest and state how the variable is distributed. (i) Determine the expected value of the random variable and interpret the expected value in context.

The random variable of interest here is the number of suspicious transactions that need to be reviewed until the first transaction is blocked. This variable follows a geometric distribution, characterized by the number of trials until the first success—in this context, "success" means identifying a transaction that gets blocked. To calculate the expected value of this random variable, we use the formula \(E(X) = \frac{1}{p}\), where \(p\) is the probability of encountering a suspicious transaction that will be blocked. If, for example, the probability \(p\) is 0.2, then the expected number of reviews before blocking one transaction is \(E(X) = \frac{1}{0.2} = 5\). This means that, on average, the specialist will need to review 5 suspicious transactions before blocking one, providing a useful benchmark for resource allocation in the transaction review process.