[機統] 加入某分布後的雜訊
假設有個1-dimensional data point x=5,
另外有個normal distribution N(3,2) with mean 3 and variance 2,
且有個變數v=3.5是從這個N(3,2)抽樣出來,
現在假設你只知道y=x+v=8.5與N(3,2)這個分布, 但是不知道x與v的值,
請問x是4的機率, 以及x是5的機率要怎麼算?
更general一點的問題是:
假設有個1-dimensional data point x,
另外有個normal distribution N(μ,σ) with mean μ and variance σ,
且有個變數v是從這個N(μ,σ)抽樣出來,
現在假設你只知道y=x+v與N(μ,σ)這個分布, 但是不知道x與v的值,
請問x是某特定值的機率要怎麼算?
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