Society of Actuaries (SOA) PA Practice Exam

Statistical convergence is best described as:

1. The process where random variables agree on an outcome

2. Random variables settling on a specific number

3. An analytical method to analyze trends

4. A data transformation technique

The correct answer is: Random variables settling on a specific number

Statistical convergence refers to the concept where a sequence of random variables becomes increasingly close to a specific value as more terms in the sequence are considered. This is often framed in the context of probability, where we say that a series of random variables converges in distribution or in probability to a particular number. In this case, the emphasis on random variables settling on a specific number captures the essence of statistical convergence. It describes the phenomenon where the values of the random variables approach a fixed limit, which can be interpreted as a deterministic number, especially in the context of sequences converging to a point such as the expected value or mean. Other options lack this specific focus on convergence towards a particular value. The idea of random variables agreeing on an outcome is more related to the concept of symmetry or consistency rather than convergence. Analyzing trends or transforming data does not inherently address the principle that underlies convergence, which is fundamentally about the relationship between random variables and their limiting behavior over time.