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Q58Section C (Section C)58 of 60

UMVUE of a Bernoulli polynomial

Let x1=1x_{1}=1, x2=0x_{2}=0, x3=0x_{3}=0, x4=1x_{4}=1, x5=0x_{5}=0, x6=1x_{6}=1 be the data on a random sample of size 66 from Bin(1,θ)\mathrm{Bin}(1,\theta) distribution, where θ∈(0,1)\theta\in(0,1). Then the uniformly minimum variance unbiased estimate of θ(1+θ)\theta(1+\theta) equals __________

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