作者love113w (Banana)
看板Statistics
標題[問題] 想請教一題機率
時間Sat Dec 24 21:43:51 2016
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.
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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
1F：→ goshfju: 用mgf做比較輕鬆 12/25 10:40
2F：推 goshfju: 剛沒看到2倍 拍謝 12/25 10:48
3F：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 12/25 11:24
4F：→ goshfju: 了 12/25 11:24
5F：→ love113w: 好 謝謝大大 已解出來了 12/27 08:16