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Relationship between relative frequency and probability of an event?
The relative frequency is an estimate of the probability of an event.
What is the difference between cumulative frequency and frequency?
nothing
What is the difference between atleast and atmost in probability?
The difference between "at least" and "at most" is not restricted to probability. The difference is simply one between the precise meaning of the phrases in every day English language.
What the difference between a probability distribution and a probability function?
None. The full name is the Probability Distribution Function (pdf).
What is difference between relative frequency and subjective frequency?
Consider a perfectly 'fair' die. The probability of throwing a two with it is 1 out of six. In fact, if you were to throw this die 1200 times you would expect the die to come up two very nearly 200 times. No matter what the actual frequency, n, might be though you would say that the relative frequency was n/1200. We would rarely speak of subjective frequency. Rather we would speak of subjective probability. Suppose you are a meteorologist attempting to convey your 'degree of belief' about whether a six-centimetre snowfall will occur this evening. There is no question that this afternoon's conditions will occur 1200 times again (at least not in your own lifetime) so that you can use a frequency approach. But you can use you own experience and knowledge of weather patterns to offer some indication of your degree of belief. You do this by saying something like, "I predict that there is a 60% probability that there will be a snowfall this evening in our region this evening." I've seen statisticians become very angry with each other over these alternative definitions of probability.
