课程: Probability Foundations for Data Science

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Weak Law of Large Numbers

Weak Law of Large Numbers

课程: Probability Foundations for Data Science

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Weak Law of Large Numbers

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- [Instructor] Next step is the weak law of large numbers. The weak law of large numbers, also known as Khinchin's Law, is a core probability limit theorem. This theorem helps describe the behavior of the average of a large number of independent and identically-distributed random variables. These are often denoted as IID random variables for short. The weak law of large numbers states the finite sample mean of a collection of independent and identically-distributed random variables converges in probability to the expected value of those variables as the sample size increases. Let's look at the formula for this. Let X1 to Xn be a sequence of independent and identically-distributed random variables. These variables have an expected value of E of X, a finite variance of var X and a sample average of Xn. The sample average can be gathered from the following equation, where you have 1 divided by N, and you multiply that by the sum of all the different Xi values between one to N. The weak…

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