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1639统计简单derivationshort

Joint MLEs in a Normal Model

题目

Suppose X1,,X9X_1,\dots,X_9 are modeled as i.i.d. N(μ,σ2)N(\mu,\sigma^2). From the sample you know that Xˉ=5,i=19(XiXˉ)2=18.\bar X = 5, \qquad \sum_{i=1}^9 (X_i-\bar X)^2 = 18. Find the MLEs of μ\mu and σ2\sigma^2.

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\hat\mu

\hat\sigma^2