[機統] 隨機變數轉換

[DFTz (..)]

請問以下兩題:


(1) Z = X+Y, r.v X~exp(1) and r.v Z~exp(1) , X and Y are independent

then what's the pdf of Y ?



(2) if X ~ F(x) = (1-exp(-2x))u(x), F(x) is the cdf of X,

let Y = (X -1)u(x-1), u(x) is step function

what's the pdf of Y ?



謝謝

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→ goshfju     :(1)用mgf去證比較快 Z=X+Y~Gamma(2,1)
→ doublewhi   :第一題是Y=Z-X  不是相加