Let X1, X2,...,Xn denote a random sample from a distribution that is N(0, θ). a) Show...

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Question

Let X1, X2,...,Xn denote a random sample from a distribution that is N(0, θ).

a) Show that Y = sigma (1 to n) Xi² is a complete sufficient statistic for θ. (solved)

b) Find the UMVUE of θ². (need help with this one)

Note: I am in particular having trouble finding out what distribution Y = sigma Xi^2 is. The professor advise us to find the second moment generating function for Y, but I not sure how I find that. Please do show work and also explanation.

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math Statistics-And-Probability

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Answer 1

Answer #1

4) To 47 0 (xi) 670 Ihr 12イ t 7i t-ス (-2 t 70 021) ng n (12 2 1 2 m (n+2 her in ei. Here we have used concepts of sampling distribution and moment generating functions. Therefore obtained umvue of the required parameter.

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Answer 2

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Let X1, X2,...,Xn denote a random sample from a distribution that is N(0, θ). a) Show...

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