If a sample size n is drawn from a population, how would you use the moment generating function to find the distrbution of the sample mean, i have derived the exponential mgf to belambda

1111111111111111111111111111111111111lambda - t

and have used that to find the mean,__1__

1111111111111111111111111111111lambda

but am unsure whether this is the distribution of the mean or not? Any help?