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Questions and Answers
Relative frequency is also known as _______________________ probability or a posteriori probability.
Relative frequency is also known as _______________________ probability or a posteriori probability.
empirical
The Law of Large Numbers states that as the number of trials increases, the relative frequency of an event will approach its _______________________ probability.
The Law of Large Numbers states that as the number of trials increases, the relative frequency of an event will approach its _______________________ probability.
true
The proportion of times an event occurs in a large number of trials is known as _______________________ relative frequency.
The proportion of times an event occurs in a large number of trials is known as _______________________ relative frequency.
long-run
Relative frequency is calculated as the number of times an event occurs (successes) divided by the total number of _______________________.
Relative frequency is calculated as the number of times an event occurs (successes) divided by the total number of _______________________.
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The relative frequency provides an estimate of the _______________________ probability of an event, which is unknown.
The relative frequency provides an estimate of the _______________________ probability of an event, which is unknown.
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As the number of trials increases, the relative frequency becomes a more accurate estimate of the _______________________ probability.
As the number of trials increases, the relative frequency becomes a more accurate estimate of the _______________________ probability.
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Study Notes
Relative Frequency (A Posteriori)
Definition:
- Relative frequency, also known as empirical probability or a posteriori probability, is the probability of an event based on the number of times it has occurred in the past.
- It is a measure of the frequency of occurrence of an event in a large number of trials.
Key Concepts:
- Long-run relative frequency: The proportion of times an event occurs in a large number of trials.
- Law of Large Numbers (LLN): States that as the number of trials increases, the relative frequency of an event will approach its true probability.
Calculation:
- Relative frequency is calculated as the number of times an event occurs (successes) divided by the total number of trials.
- Formula:
Relative Frequency = (Number of Successes) / (Total Number of Trials)
Example:
- A coin is flipped 100 times, and heads come up 55 times.
- Relative frequency of getting heads = 55/100 = 0.55
Interpretation:
- The relative frequency is a measure of how often an event occurs in the long run.
- It provides an estimate of the true probability of an event, which is unknown.
- As the number of trials increases, the relative frequency becomes a more accurate estimate of the true probability.
Advantages:
- Relative frequency is based on actual data and is a more objective measure of probability.
- It is useful for estimating probabilities in situations where the true probability is unknown.
Limitations:
- Relative frequency is sensitive to the number of trials and can be affected by chance fluctuations.
- It may not accurately reflect the true probability of an event, especially with small sample sizes.
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Description
Learn about relative frequency, also known as empirical probability, which is a measure of the frequency of occurrence of an event in a large number of trials. Understand its calculation, interpretation, advantages, and limitations.
