# Distribution of the sample mean of an exponential distribution

 P: 2 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.
 Sci Advisor P: 3,313 You need to compute the five fold convolution of the exponential distribution. Have you studied convolutions?
P: 2,504
 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?

 P: 2 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.