# Thread: What is variance of X-bar^2, if X ~ N(theta, sigma^2), sigma is known?

1. ## What is variance of X-bar^2, if X ~ N(theta, sigma^2), sigma is known?

I want to calculate variance of X-bar^2, (mean of X)^2,
when Xi ~ Normal(theta, sigma^2) and sigma is known. plz help.

2. ## Re: What is variance of X-bar^2, if X ~ N(theta, sigma^2), sigma is known?

Hi! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

3. ## Re: What is variance of X-bar^2, if X ~ N(theta, sigma^2), sigma is known?

Originally Posted by Yihyunsoo
I want to calculate variance of X-bar^2, (mean of X)^2,
when Xi ~ Normal(theta, sigma^2) and sigma is known. plz help.
Hint: Use the normal pdf and obtain the 2nd and 4th moments for X and then use the definition of variance. (keep in mind that the variance of the estimate --x-bar--- is just scaled by the sample size, n).

4. ## Re: What is variance of X-bar^2, if X ~ N(theta, sigma^2), sigma is known?

thank you! i solved it. and keep in mind the guidelines. ^^

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