(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.

Question

UpStudy AI · Accepted Answer

To solve this problem, let's break it down step by step.

### (i) Define the random variable of interest and state how the variable is distributed.

1. **Random Variable Definition**:
   Let $$ X $$ be the random variable representing the number of suspicious transactions that need to be reviewed until the first transaction that is blocked.

2. **Distribution**:
   The random variable $$ X $$ follows a **geometric distribution**. This is because we are interested in the number of trials (transactions reviewed) until the first success (the first blocked transaction). The geometric distribution is characterized by the probability of success $$ p $$ on each trial.

### (ii) Determine the expected value of the random variable and interpret the expected value in context.

The expected value $$ E(X) $$ of a geometrically distributed random variable can be calculated using the formula:

$$
E(X) = \frac{1}{p}
$$

where $$ p $$ is the probability of success (the probability that a transaction is blocked).

#### Interpretation:
- The expected value $$ E(X) $$ represents the average number of suspicious transactions that need to be reviewed before encountering the first blocked transaction. 
- For example, if $$ p = 0.1 $$ (meaning there is a 10% chance that any given transaction will be blocked), then:

$$
E(X) = \frac{1}{0.1} = 10
$$

This means, on average, the specialist would need to review 10 suspicious transactions before finding one that is blocked.

If you have a specific value for $$ p $$, please provide it, and I can calculate the expected value for you.
The random variable $$ X $$ represents the number of suspicious transactions reviewed until the first blocked transaction and follows a geometric distribution. The expected value $$ E(X) $$ is $$ \frac{1}{p} $$, where $$ p $$ is the probability of a transaction being blocked. This means, on average, you would need to review $$ \frac{1}{p} $$ transactions to find the first blocked one.

Upstudy AI Solution

Answer

Solution

(i) Define the random variable of interest and state how the variable is distributed.

(ii) Determine the expected value of the random variable and interpret the expected value in context.

Interpretation:

Bonus Knowledge

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