## Distribution of the sample mean of an exponential distribution

Let's say you have a random sample of 5 values that are drawn from an exponential distribution with a mean of 8.

How do I find the distribution of Ybar, which is the sample mean of the 5 random variables? [Note: Ybar = 1/5(Y₁+Y₂+Y₃+Y₄+Y₅)]

I know that for an exponential distribution with mean 8 (i.e. Y~exp(8)), the variance would be 64.
So it seems like the distribution of Ybar can't also be exponential, since the variance is supposed to be the mean squared. I figure the mean of Ybar will be 8, but the variance must be something other than 64.
I don't know what approach to take...this seems harder than the approach for a normal distribution.
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 Quote by buggy418 How do I find the distribution of Ybar, which is the sample mean of the 5 random variables? [Note: Ybar = 1/5(Y₁+Y₂+Y₃+Y₄+Y₅)] So it seems like the distribution of Ybar can't also be exponential
True. What distribution would you expect for the sample means?

## Distribution of the sample mean of an exponential distribution

I think it may have a gamma distribution of some sort. We've learned the method of distribution functions. So maybe if I let V=5Y, and then found the distribution of V/5 that would work? But it seems like that's just going to make me end up at the exponential distribution again, since V/5 = 5Y/5 = Y.

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