[問題] 想請教一題機率

[love113w (Banana)]

A device containing two key components fails when, and only when, both
components fail.
The lifetimes,  T1 and  T2 of these components are independent with
common density function

                -t
        f(t)={ e   ,  0<t
             { 0   ,  otherwise

The cost, X, of operating the device until failure is 2T1+T2 . Let g be
the density function for X.
Determine g(x), for x > 0.
---------------------------------------------------------

我的想法 :

Let X=2T1+T2
    Y=T2

f  (x,y)=f  (t1,t2) |J|
 X,Y       T1,T2

        =f( (x-y)/2 , y ) * 2

        =e^-(x-y)/2 * e^-y * 2

然後再去把y積分掉 從0~無限大

不知道這樣錯在哪裡? 請求幫忙

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※ 編輯: love113w (111.248.24.165), 12/24/2016 21:44:32
※ 編輯: love113w (111.248.24.165), 12/24/2016 21:45:16
→ goshfju: 用mgf做比較輕鬆
推 goshfju: 剛沒看到2倍 拍謝
推 goshfju: 你要習慣在pdf後面寫出變數的範圍 不然後續很容易就算錯
→ goshfju: 了
→ love113w: 好 謝謝大大 已解出來了