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February 4th, 2013, 05:30 PM  #1 
Member Joined: May 2012 Posts: 56 Thanks: 0  A question about statistics...
Let X1, X2, …, Xn be a random sample from a Poisson(?) distribution. Let be their sample mean and their sample variance. a) Show that and both have a standard normal limiting distribution. b) Find the limiting distribution of c) Find the limiting distribution of a) For , we know that = . Since appraches N(0,1) in distribution by CLT, and since appraches 1 in probability, the whole thing approaches N(0,1). For , we get the same result...since the mean is equal to the variance in a poisson distribution. b) I'm a little confused about this one... c) From a theorem in my textbook, I know that if and if there is a differentiable function g(x) at theta where the derivative at theta is not zero...then . So I just need to use this theorem, right? And in this case g(x)=x^2. Do you think my answer for a), and c) are correct? Also, can you give me a hint for b)? Thanks in advance 

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