Law of Large Numbers Statistics Example 1
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Example 1
easyA coin is flipped and the running proportion of heads is recorded: After 10 flips: 0.70, after 50: 0.56, after 200: 0.52, after 1000: 0.498, after 10,000: 0.5012. What does this pattern illustrate?
Solution
- 1 Step 1: The proportion of heads starts far from 0.5 (at 0.70 with just 10 flips).
- 2 Step 2: As the number of flips increases, the proportion gets closer and closer to 0.5: 0.70 → 0.56 → 0.52 → 0.498 → 0.5012.
- 3 Step 3: This illustrates the law of large numbers: as the number of trials increases, the experimental probability (relative frequency) converges toward the theoretical probability.
Answer
This illustrates the law of large numbers — the proportion of heads converges toward the theoretical probability of 0.5 as the number of flips increases.
The law of large numbers states that the average of results from a large number of independent trials gets closer to the expected value as more trials are performed. This is why experimental probability becomes more reliable with more data.
About Law of Large Numbers
The Law of Large Numbers states that as the number of independent, identically distributed trials increases, the sample average converges to the theoretical expected value (population mean). In other words, larger samples produce more reliable estimates of the true probability or average.
Learn more about Law of Large Numbers →More Law of Large Numbers Examples
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