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Math Help - sample mean

  1. #1
    Yan
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    sample mean

    show that if the two samples come from normal populations, then sample mean1 - sample mean2 is a random variable having a normal distribution with the mean1 - mean2 and variance1/n1 + variance2/n2.
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  2. #2
    Flow Master
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    Quote Originally Posted by Yan View Post
    show that if the two samples come from normal populations, then sample mean1 - sample mean2 is a random variable having a normal distribution with the mean1 - mean2 and variance1/n1 + variance2/n2.
    You should start by finding the distribution of the sample mean \overline{X}_1 (and hence \overline{X}_2).

    I think this is done somewhere in MHF - you will have to search for it. Alternatively, I'm sure it will be somewhere on the web and certainly many textbooks do it. And you could always have a go at doing it yourself. If you're truly stuck with this, please say so (after you've made an effort to try and find it).

    Then use the usual formulae for finding E\left( \overline{X}_1 - \overline{X}_2\right) and Var\left( \overline{X}_1 - \overline{X}_2\right) .
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