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Q44Section C (Section C)44 of 60

Constant in a paired-difference variance estimator

Let {Xk}k≥1\{X_k\}_{k\ge 1} be a sequence of i.i.d. random variables with E(X1)=μ\mathbb{E}(X_1)=\mu and Var(X1)=σ2<∞\mathrm{Var}(X_1)=\sigma^2<\infty. Suppose cc is a constant that does not depend on nn such that cn∑i=1n(X2i−X2i−1)2\frac{c}{n}\sum_{i=1}^n(X_{2i}-X_{2i-1})^2 is a consistent estimator of σ2\sigma^2. Then cc is equal to __________ (round off to 2 decimal places)

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