(New page: In response to Brian, theoretically, if you took <math>\lim_{n\to\infty}</math>, then the average of all of the wages would be unaffected by having one person earning greater than the aver...) |
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In response to Brian, theoretically, if you took <math>\lim_{n\to\infty}</math>, then the average of all of the wages would be unaffected by having one person earning greater than the average. If an infinite number of people have what is considered to be the "average", and then one person is above average, the limit still results in the original "average". | In response to Brian, theoretically, if you took <math>\lim_{n\to\infty}</math>, then the average of all of the wages would be unaffected by having one person earning greater than the average. If an infinite number of people have what is considered to be the "average", and then one person is above average, the limit still results in the original "average". | ||
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BUT, can you have an infinite number of people and thus use a limit here? I'd say no, because the # of people is a discrete value no matter how large it is. This is in contrast to a non-discrete value like numbers in between 0 and 1. That might be what the problem is getting at (either that or there's some other proof that relates to continuous RVs). n isn't defined, but I would argue that even if it is an unknown quantity, it is always going to be finite. | BUT, can you have an infinite number of people and thus use a limit here? I'd say no, because the # of people is a discrete value no matter how large it is. This is in contrast to a non-discrete value like numbers in between 0 and 1. That might be what the problem is getting at (either that or there's some other proof that relates to continuous RVs). n isn't defined, but I would argue that even if it is an unknown quantity, it is always going to be finite. | ||
Latest revision as of 15:24, 12 October 2008
In response to Brian, theoretically, if you took $ \lim_{n\to\infty} $, then the average of all of the wages would be unaffected by having one person earning greater than the average. If an infinite number of people have what is considered to be the "average", and then one person is above average, the limit still results in the original "average".
BUT, can you have an infinite number of people and thus use a limit here? I'd say no, because the # of people is a discrete value no matter how large it is. This is in contrast to a non-discrete value like numbers in between 0 and 1. That might be what the problem is getting at (either that or there's some other proof that relates to continuous RVs). n isn't defined, but I would argue that even if it is an unknown quantity, it is always going to be finite.
