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distribution of random variables
Posted: November 23rd, 2003, 6:06 am
by VinceMancini
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
Posted: November 24th, 2003, 9:30 am
by VinceMancini
anybody ?
distribution of random variables
Posted: November 24th, 2003, 12:59 pm
by Marsden
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
Posted: November 24th, 2003, 1:35 pm
by MikeM
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.
distribution of random variables
Posted: November 25th, 2003, 5:25 am
by VinceMancini
distribution of random variables
Posted: November 25th, 2003, 5:31 am
by VinceMancini
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.
distribution of random variables
Posted: November 25th, 2003, 5:31 am
by VinceMancini
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.