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A sampling distribution function is a probability distribution function. Wikipedia gives this definition: In statistics, a sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample). I would add that the sampling distribution is the theoretical pdf that would ultimately result under infinite repeated sampling. A sample is a limited set of values drawn from a population. Suppose I take 5 numbers from a population whose values are described by a pdf, and calculate their average (mean value). Now if I did this many times (let's say a million times, close enough to infinity) , I would have a relative frequency plot of the mean value which will be very close to the theoretical sampling pdf.

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Q: What is the difference between a probability distribution and sampling distribution?
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