The Law of Large Numbers (LLN) is a fundamental theorem in probability theory. Which of the following is a correct interpretation of the LLN?
A) The LLN states that as the number of independent trials increases, the sample mean will converge to the population median.
B) The LLN guarantees that in a large number of trials, the sample mean will exactly equal the population mean.
C) The LLN states that as the sample size increases, the sample mean will converge to the expected value of the population mean.
D) The LLN implies that the variance of the sample mean increases with the sample size.