central limit theorem

**winganger** · Apr 27th 2008, 08:03 AM

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.

**CaptainBlack** · Apr 27th 2008, 08:31 AM

Originally Posted by winganger

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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