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July 27th, 2010, 01:38 PM   #1
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random sample from an exponential distribution?

So there is a theorem in the book that goes like this:

If we sample from a NORMAL DISTRIBUTION with mean u and variance b, then the distribution of the sample mean is N(u, b/n).

But there is a couple of problems in which the random sample comes from other types of distributions, like:

Let X be the mean of a random sample of size n = 36 from an exponential distribution with mean 4. Approximate P(3.1 < X 4.6).

I don't know what to do since this sample comes from an exponential distribution and not the normal distribution.
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July 29th, 2010, 04:00 PM   #2
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Re: random sample from an exponential distribution?

Quote:
Originally Posted by oahz
So there is a theorem in the book that goes like this:

If we sample from a NORMAL DISTRIBUTION with mean u and variance b, then the distribution of the sample mean is N(u, b/n).

But there is a couple of problems in which the random sample comes from other types of distributions, like:

Let X be the mean of a random sample of size n = 36 from an exponential distribution with mean 4. Approximate P(3.1 < X 4.6).

I don't know what to do since this sample comes from an exponential distribution and not the normal distribution.
The density function for an exponential function with mean m is given by [exp(-x/m)]/m for x ? 0. The variance is mē.

For your problem, the standard deviation for one sample is 4, while for n=36, it is 2/3. You can use the data for a normal distribution to approximate the probability you are looking for. There is an approach which could lead to an exact answer, but it is much more complicated.
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