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- VinceMancini
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distribution of random variables
A simple question for most of you chaps: say we have X1, X2, ...........XN taken from a population whose pdf is (say) a Gamma dist'n. Can we say anything at all about the pdf of the individual random variables ......... the pdf of X1 ?
distribution of random variables
If the Xi-s are chosen randomly and not ordered, then don't they each just have the same distribution as the population?
distribution of random variables
I like Marsden's answer. ...You could also apply the central limit theorem to some sample statistic, e.g. SUM[Xi - Mean(i)]/sqrt(SUM[var(i)])) approaches a normal distribution.
Last edited by MikeM on November 23rd, 2003, 11:00 pm, edited 1 time in total.
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- VinceMancini
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distribution of random variables
Last edited by VinceMancini on November 24th, 2003, 11:00 pm, edited 1 time in total.
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- VinceMancini
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distribution of random variables
QuoteOriginally posted by: MikeMI like Marsden's answer. ...You could also apply the central limit theorem to some sample statistic, e.g. SUM[Xi - Mean(i)]/sqrt(SUM[var(i)])) approaches a normal distribution.yes, but that would be a statistic pdf , not applicable to an individual random variable pdf. for example using CLT the pdf of the sample mean will be approximately normal, but the random variable pdf can be anything at all.
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- VinceMancini
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distribution of random variables
QuoteOriginally posted by: MarsdenIf the Xi-s are chosen randomly and not ordered, then don't they each just have the same distribution as the population?thats what I thought. thank you Marsden, MikeM.