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Let X_1, ..., X_n be a random sample from a normal distribution, N(0, theta). Is theta_hat...

Let X_1, ..., X_n be a random sample from a normal distribution, N(0, theta). Is theta_hat a UMVUE of theta?

The above question is from chapter 9 problem 23b of Introduction to Probability and Mathematical Statistics (for which you have a solution posted on this website). I'm confused about the part in the posted solution where we go from the line that says E(x^4 -2\theta * E(x^2) + E(\theta^2) to the line that says (3\theta^2-2\theta^2+\theta^2). Could you please explain this to me?

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Answer #1

so basically

we need to show

Z^2 follow chi-square distribution

hence

=2 + 1

= 3

hence

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