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Simple Random Sampling
In Simple Random Sampling each possible sample has an equal chance of being selected. Further, each item in the entire population also has an equal chance of being selected.
Example A retailer of electronic goods (TVs, Stereos, Videos) wants to study her customer purchases in the city of Mumbai. For this purpose her population is all her customers in Mumbai. Their names and addresses are on the carbon copies of bills in her bill book. To do a Random Sampling of her customers she can put all the carbon copies in a box and draw out a certain number of copies after thoroughly mixing them up. The customers so picked would form a Random Sample. In a more refined manner, she can enter the bill numbers in her computer and command it to select bill number at random. The customers related to the bill numbers so selected would form a Random Sample. (If she wanted a judgemental sample she would have scrutinized the bill copies and selected certain customers whom she considered a representative sample. However, the accuracy of the estimate so made cannot be found.)
Example
A retailer of electronic goods (TVs, Stereos, Videos) wants to study her customer purchases in the city of Mumbai. For this purpose her population is all her customers in Mumbai. Their names and addresses are on the carbon copies of bills in her bill book. To do a Random Sampling of her customers she can put all the carbon copies in a box and draw out a certain number of copies after thoroughly mixing them up. The customers so picked would form a Random Sample.
In a more refined manner, she can enter the bill numbers in her computer and command it to select bill number at random. The customers related to the bill numbers so selected would form a Random Sample.
(If she wanted a judgemental sample she would have scrutinized the bill copies and selected certain customers whom she considered a representative sample. However, the accuracy of the estimate so made cannot be found.)
An approximation to the error of a Riemannian sum: where V g (a; b) is the total variation of g on [a, b] de ned by the sup over all partitions on [a, b], including (a; b
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