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Math Help - mean and variance of population distribution - law of large numbers - plz help

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    mean and variance of population distribution - law of large numbers - plz help

    A population distribution has a mean of 10 and a variance of 16. Determine the mean and variance of Ybar from an i.i.d. sample from this population for a) n=10, b) n= 100 and c) n=1000. Relate the answers to the law of large numbers.

    Please advise how to start this question?
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    Re: mean and variance of population distribution - law of large numbers - plz help

    Quote Originally Posted by homalina View Post
    A population distribution has a mean of 10 and a variance of 16. Determine the mean and variance of Ybar from an i.i.d. sample from this population for a) n=10, b) n= 100 and c) n=1000. Relate the answers to the law of large numbers.

    Please advise how to start this question?
    For iid  Y_1,\cdots, Y_n with mean and variance \mu\;&\;\sigma^2
    \bar{Y}=\dfrac{1}{n}\sum_{i=1}^n Y_i=\mu

    E[\bar{Y}]=\dfrac{1}{n}\sum_{i=1}^n E[Y_i]=\mu

    also, Var(\bar{Y})=\dfrac{1}{n^2}\sum_i {\sigma_i}^2=...
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    Re: mean and variance of population distribution - law of large numbers - plz help

    Thanks a lot
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