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Q44Section C (Section C)44 of 60

Constant for unbiased normal scale estimation

Let X1,X2,…,X10X_1, X_2, \dots, X_{10} be a random sample from an N(0,σ2)N(0, \sigma^2) distribution, where σ>0\sigma > 0 is an unknown parameter. For some real constant cc, let Y=c10∑i=110∣Xi∣Y = \frac{c}{10}\sum_{i=1}^{10} |X_i| be an unbiased estimator of σ\sigma. Then, the value of cc equals __________ (round off to two decimal places)

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