# Law Of Large Numbers Essay

Introduction

Flipping a coin is a simple action most people have seen or done. But what results would one yield if they flipped a coin one hundred time. The Law of Large Numbers addresses the results that are almost certain. The Law of Large Numbers is “A law expressing the fact that if a trial in which all outcomes are independent of each other and equally likely is repeated, then the relative frequency of each outcome approximates its probability with increasing accuracy as the number of repetitions becomes sufficiently large” is the definition given for law of large numbers (Law of Large Numbers).

The application of weak law of large

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Since the number of tails flipped is larger than the number of heads flipped the final average is below the theoretical mean. One can find that these results are statistically significant with a P-Value < 0.01 when statistically analyzing the results.

Discussion

The predictions of the law of large numbers agree with the graph created. The mean of the flips regresses toward the value 0.5 as the number of flips done increases. Not achieved was the true mean, µ, of the coin landing tails or heads (50%). However, the results were close enough to 50% to be considered statistically significant. The hypothesis stated in the introduction is therefore true. The cumulative number of heads is never greater than 0.5; however, it is equal to 0.5 several times which is a noteworthy feature of the data.

Just as the article done by Falk and Lann predicts, as the sample size increases the results regress toward the mean. This is clearly shown in the graph above, with the cumulative number of heads approaching the predicted probability. If the experiment was continued, the line would approach closer and closer to the predicted