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Law of Large Numbers
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A basketball player with a free-throw success rate of 70% misses most shots in a practice session.
Given a large enough number of shots, the player's success rate will converge to their average rate of 70%, illustrating the law of large numbers.
Flipping a fair coin 50 times and getting an uneven distribution of heads and tails.
As the number of coin flips increases to a large number, the proportion of heads to tails will approach a 1:1 ratio, demonstrating the law of large numbers.
The average height of 10 randomly chosen people is notably different from the population average.
As the sample size of randomly chosen people is increased, the sample's average height will likely approach the true population average, as per the law of large numbers.
A pizzeria's nightly earnings are highly inconsistent during its first month of business.
Over a greater time span, the pizzeria's earnings are expected to converge on a certain average value, consistent with the law of large numbers.
A factory's daily production varies greatly from the monthly average after only a week.
As the factory continues production over a longer period, the daily variations will average out to the expected monthly production, in accordance with the law of large numbers.
Sampling a substance's temperature at different times results in a wide range of measurements.
Increased frequency and number of temperature measurements will result in an average value that more accurately reflects the true temperature of the substance, in line with the law of large numbers.
A die is rolled 20 times, but the number 6 appears less often than expected.
With more rolls, the frequency of all numbers, including 6, will align closer to the theoretical probability of 1/6, which is predicted by the law of large numbers.
An investor sees substantial fluctuation in returns over a few days.
As the number of investment days grows, the average returns are expected to stabilize and reflect the long-term average return due to the law of large numbers.
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