So my prof. has not replied to my e-mail, so I was wondering if someone here can help me understand why the MLE for a random variable X~Unif(-θ,θ) is max|X(adsbygoogle = window.adsbygoogle || []).push({}); _{i}|. Attached is the problem as well as my attempt for the solution.

Here is my thought process:

Upon sketching the graph, I thought the answer would be min( |min(X_{i})|, |max(X_{i})| ) because there are two different tails and the one closer to zero should have the highest value for L(θ). So if |min(X_{i})| < |max(X_{i})|, then L(θ = min(X_{i})) > L(θ = max(X_{i})), which would make min(X_{i}) the MLE for θ.

Whether or not this gets answered in time before my exam, I'd still be curious to know the reasoning for the correct answer :)

Thanks a bunch!

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# MLE for Uniform(-A,A) - exam today!

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