The law of large numbers lln is a fundamental theorem in...

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.

Transcript

00:01 In your question, you're asked to choose the correct definition of the law of large numbers.

00:05 So i'm going to go through each of your choices here and explain whether it is law of large numbers or not, or what it is relating to.

00:13 So the law of large numbers, if we look at this first statement, says if the sample size is large enough, the distribution of the sample mean will be nearly normal.

00:26 That is not the law of large numbers.

00:27 The law of large numbers plays a role in that, but that first option is referring to what we call the central limit theorem, or clt.

00:37 The law of large numbers itself is not talking about normality distributions, but the central limit theorem is.

00:45 So the first answer choice is not correct.

00:47 It's making a reference to the central limit theorem.

00:50 I'm going to jump down to the third choice here.

00:52 The third choice says the probability that an event will occur is derived from one's increasing knowledge of relevant circumstances.

01:00 Well, that's a true statement.

01:02 If we know more about the relative circumstance, the probability of that event is determined by our knowledge of those circumstances.

01:14 For example, how many different possible outcomes.

01:17 But that has nothing to do with the law of large numbers.

01:19 It has nothing to do with increasing the trials or the experiment or anything.

01:25 So that's more along the lines of how we could feel confident in a probability calculation just in general by having knowledge of the circumstances.

01:37 That is out.

01:40 The fourth one says the probability of obtaining a favorable outcome increases as the number of trials increase.

01:48 That is just flat out wrong, and it doesn't relate to any probability knowledge that we might have.

01:58 The probability of a favorable outcome means what we want to happen would happen...

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