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Math Help - central limit theorem

  1. #1
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    central limit theorem

    Suppose that the sizes (in KB) of email messages
    Xn in a mailbox are independent
    and identically distributed according to a geometric distribution with sample space
    SX = {0,1,2,...} .

    Suppose that the average size of
    an email message is 2KB. If the total number of email messages in the mailbox is 550, use the central limit to theorem to estimate the required size of the mailbox so that it can hold all of the messages with 90% probability.

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by winganger View Post
    Suppose that the sizes (in KB) of email messages
    Xn in a mailbox are independent

    and identically distributed according to a geometric distribution with sample spaceSX = {0,1,2,...} .

    Suppose that the average size of
    an email message is 2KB. If the total number of email messages in the mailbox is 550, use the central limit to theorem to estimate the required size of the mailbox so that it can hold all of the messages with 90% probability.
    The CLT tell you that the asymtotic distribution of the total size of 550 emails is normal with mean:

    \mu_{550}=550 \times \mu

    and variance:

    \sigma_{550}=550 \times \sigma

    where \mu is the mean size of a email, and \sigma^2 is the variance of the size of an email.

    You are given \mu, which is sufficient for you to find \sigma^2 as you are told that the size has a geometric distribution, which gives you sufficient information to answer this question.

    RonL
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