Difference between frequency distibution and probability distribution
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This is actually a good question. Probability and frequency are closely related but not the same thing. I’ll try to explain:
Probability
The definition of probability used by nearly all mathematicians and statisticians is the following:
"Probability is a number P(E) associated with an event E (e.g. an outcome of an experiment) which satisfies certain axiomatic properties."
In lay terms, probability is a number between 0 and 1.0 indicating the likelihood of an event. An event that cannot occur has probability P(E) = 0, an event that is certain to occur has P(E) = 1, and an event that is equally likely to occur or not has P(E) = 0.5. Probabilities are always related to an associated exposure period, e.g. a mission, a project, a year, etc.
There are two interpretations of probability commonly used. The first is the frequentist interpretation. This defines probability as the number of times an event occurs divided by the number of opportunities for it to occur. The result of this calculation is called the “relative frequency” of the event. When there is no fixed value for the number of opportunities, an event's probability is defined as the limit of its relative frequency in a large number of opportunities. If the event E occurs n times in N opportunities, its probability P(E) is estimated as n/N. The estimate is assumed to converge on the true probability as the number of opportunities tends to infinity.
The limitation of the relative frequency interpretation is that it only applies to situations for which relative frequency data exist. It does not apply to unique situations that will be encountered only once.
The second interpretation is subjective probability. In this interpretation, an event's probability is the degree of belief that the event will occur. Subjective probabilities are personal judgments based on all of the assessor's previous experience relevant to the situation at hand. Previous experience may include relative frequency data, but the probability is still subjective.
Any values may be assigned to subjective probabilities that are consistent with the axioms of probability. For example, if one assumes P(E) = 0.6, one must also assume P(not E) = 0.4.
Frequency
Relative frequency is an important concept in the definition of probability as I explained above.
Frequency is also employed to mean the number of events per unit time or other measure of exposure. For example, the frequency of pipeline leaks might be expressed per kilometer per year, while the frequency of occupational accidents might be expressed per 100,000 hours worked. Frequency in these usages is the number of events divided by an exposure expressed in some units of measurement.
Hope that helps!
Probability
The definition of probability used by nearly all mathematicians and statisticians is the following:
"Probability is a number P(E) associated with an event E (e.g. an outcome of an experiment) which satisfies certain axiomatic properties."
In lay terms, probability is a number between 0 and 1.0 indicating the likelihood of an event. An event that cannot occur has probability P(E) = 0, an event that is certain to occur has P(E) = 1, and an event that is equally likely to occur or not has P(E) = 0.5. Probabilities are always related to an associated exposure period, e.g. a mission, a project, a year, etc.
There are two interpretations of probability commonly used. The first is the frequentist interpretation. This defines probability as the number of times an event occurs divided by the number of opportunities for it to occur. The result of this calculation is called the “relative frequency” of the event. When there is no fixed value for the number of opportunities, an event's probability is defined as the limit of its relative frequency in a large number of opportunities. If the event E occurs n times in N opportunities, its probability P(E) is estimated as n/N. The estimate is assumed to converge on the true probability as the number of opportunities tends to infinity.
The limitation of the relative frequency interpretation is that it only applies to situations for which relative frequency data exist. It does not apply to unique situations that will be encountered only once.
The second interpretation is subjective probability. In this interpretation, an event's probability is the degree of belief that the event will occur. Subjective probabilities are personal judgments based on all of the assessor's previous experience relevant to the situation at hand. Previous experience may include relative frequency data, but the probability is still subjective.
Any values may be assigned to subjective probabilities that are consistent with the axioms of probability. For example, if one assumes P(E) = 0.6, one must also assume P(not E) = 0.4.
Frequency
Relative frequency is an important concept in the definition of probability as I explained above.
Frequency is also employed to mean the number of events per unit time or other measure of exposure. For example, the frequency of pipeline leaks might be expressed per kilometer per year, while the frequency of occupational accidents might be expressed per 100,000 hours worked. Frequency in these usages is the number of events divided by an exposure expressed in some units of measurement.
Hope that helps!
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