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How would I show that $f(x;\theta) = \frac1{2\theta}$ where $x$ is between positive and negative $\theta$ and $\theta$ is between $0$ and $\infty$ is NOT a complete family?

I know that I need to find a non-zero function $u(x)$ whose expectation will be $0$, but I am struggling with finding this function.

Thanks

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    Let $X$ be a random variable whose distribution is known to be one of these. Then by symmetry $E(X)=0$.2012-02-06

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Hint: try a function $u(x)$ which is odd, i.e., with $u(-x) = -u(x).$

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    @clarkson: all the expansion coefficients are 0 but the function is not zero so the family is not complete.2014-04-23