f(x) = Ae^(-|x|)
(1)
∫(-∞->+∞) f(x) dx =1
A∫(-∞->0) e^x dx +A∫(0->+∞) e^(-x) dx =1
2A = 1
A=1/2
(2)
P(0 =∫(0->1) f(x) dx =(1/2) ∫(0->1) e^(-x) dx = -(1/2)[ e^(-x) ]|(0->1) =(1/2)[ 1 - e^(-1) ] (3) case 1: x≤0 F(X) = ∫(-∞->x) f(t) dt = (1/2)∫(-∞->x) e^t dt = (1/2) e^x case 2: x>0 F(X) = ∫(-∞->x) f(t) dt =(1/2)∫(-∞->0) e^t dt + (1/2)∫(0->x) e^(-t) dt = 1/2 + (1/2)[ 1- e^(-x) ] =1 - (1/2)e^(-x)
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