概率论，求大神！
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F(x)
=Ae^x , x<0
=B , 0≤x<1
= 1- Ae^[-(x-1)] , x≥1
(1)
f(x)
=F'(x)
=Ae^x , x<0
=0 , 0≤x<1
= Ae^[-(x-1)] , x≥1
∫ (-∞->+∞) f(x) =1
∫ (-∞->0) Ae^x dx + ∫ (1->+∞) Ae^[-(x-1)] =1
A[e^x]|(-∞->0) - A [ e^[-(x-1)] ] |(1->+∞) =1
A +A=1
A = 1/2
lim(x->0-) F(x) = A =1/2
lim(x->0+) F(x) = B
lim(x->1-) F(x) =B
lim(x->1+) F(x) = 1-A =1-1/2 = 1/2
=> B= 1
ie (A,B)= (1/2, 0)
(2)
f(x)
=F'(x)
=(1/2)e^x , x<0
=0 , 0≤x<1
= (1/2)e^[-(x-1)] , x≥1
(3)
P(X >1/3)
=1- P(X≤1/3)
= 1- F(1/3)
=1 -1/2
=1/2
=Ae^x , x<0
=B , 0≤x<1
= 1- Ae^[-(x-1)] , x≥1
(1)
f(x)
=F'(x)
=Ae^x , x<0
=0 , 0≤x<1
= Ae^[-(x-1)] , x≥1
∫ (-∞->+∞) f(x) =1
∫ (-∞->0) Ae^x dx + ∫ (1->+∞) Ae^[-(x-1)] =1
A[e^x]|(-∞->0) - A [ e^[-(x-1)] ] |(1->+∞) =1
A +A=1
A = 1/2
lim(x->0-) F(x) = A =1/2
lim(x->0+) F(x) = B
lim(x->1-) F(x) =B
lim(x->1+) F(x) = 1-A =1-1/2 = 1/2
=> B= 1
ie (A,B)= (1/2, 0)
(2)
f(x)
=F'(x)
=(1/2)e^x , x<0
=0 , 0≤x<1
= (1/2)e^[-(x-1)] , x≥1
(3)
P(X >1/3)
=1- P(X≤1/3)
= 1- F(1/3)
=1 -1/2
=1/2
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追问
我那么算错在哪了😂
追答
我那么算错在哪了
F(∞) =1
lim(x->∞) [ 1- Ae^[-(x-1)]] =1
1=1
不是 ：F（1） =1
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