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Math Help - Sample mean PDF

  1. #1
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    Sample mean PDF

    I read a proof which showed that if X follows a normal distribution with mean \mu and variance \sigma^2 then the sample mean also follows a normal distribution with mean \mu and variance \frac{\sigma^2}{n}, is this true in the general case so that if a random variable Y has a probability density function which is a function of mean, variance and y: P(y,\mu,\sigma^2) then the sample mean is distributed according to P(\bar{y},\mu,\frac{\sigma^2}{n})
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  2. #2
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    Re: Sample mean PDF

    Quote Originally Posted by Shakarri View Post
    I read a proof which showed that if X follows a normal distribution with mean \mu and variance \sigma^2 then the sample mean also follows a normal distribution with mean \mu and variance \frac{\sigma^2}{n}, is this true in the general case so that if a random variable Y has a probability density function which is a function of mean, variance and y: P(y,\mu,\sigma^2) then the sample mean is distributed according to P(\bar{y},\mu,\frac{\sigma^2}{n})
    No, asymtotically for large n the distribution is N(\mu,\sigma^2/n) it's the Central Limit Theorem.

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