Question

To evaluate its customers' satisfaction, a bank makes a list of all the accounts. A Monte Carlo method is used to choose a random number between 1 and N, where N is the total number of bank accounts. Say, we generate a Uniform(0,N) variable X and sample an account number [X] from the list. Similarly, we choose the second account, uniformly distributed among the remaining N - 1 accounts, etc., until we get a sample of the desired size n. This is a simple random sample.

Answer 1

The student's question pertains to the use of the Monte Carlo method for simple random sampling in a statistical context, relevant to probability and statistics in college-level mathematics.

Step-by-step explanation:

The student's question involves the use of a Monte Carlo method to perform simple random sampling in a banking context. The method described involves selecting a random sample of size n from a population of size N, where N is the total number of bank accounts.

A random variable X is generated uniformly between 0 and N, and the account corresponding to the integer part of X ([X]) is chosen. The process repeats for subsequent selections with the pool size decreasing by one after each draw, to ensure that no account is selected more than once.

This procedure is consistent with basic principles of probability and statistics, particularly with regards to the formation of sampling distributions. As stated, when sample sizes increase, the sampling distribution of the mean will tend to approximate a normal distribution, according to the Central Limit Theorem.