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Q58Section C (Section C)58 of 60

MLE of a symmetric uniform half-width

Let X1,X2,…,X10X_1,X_2,…,X_{10} be a random sample from a U(−θ,θ)U(-\theta,\theta) distribution, where θ∈(0,∞)\theta\in(0,\infty). Let X(10)=max⁡{X1,X2,…,X10}X_{(10)}=\max\{X_1,X_2,…,X_{10}\} and X(1)=min⁡{X1,X2,…,X10}X_{(1)}=\min\{X_1,X_2,…,X_{10}\}. If the observed values of X(10)X_{(10)} and X(1)X_{(1)} are 88 and −10-10, respectively, then the maximum likelihood estimate of θ\theta is equal to __________ (answer in integer)

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