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3082统计中等derivationmedium

One Missing Observation Then Update

题目

A local-level model satisfies xt=xt1+wtx_t=x_{t-1}+w_t with wtN(0,3)w_t\sim N(0,3), and observations have noise variance 5. After the last filtered state N(1,9)N(-1,9), there are 1 consecutive missing observations. Then you observe a new value y=2y=2. Compute the variance just before the new observation and the updated mean/variance after processing it.

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你的答案

Variance just before observation (P-)

Updated mean (m+)

Updated variance (P+)