φ(x)
=cx ; 0≤x≤1
=0 ; elsewhere
(1)
∫(0->1) cx dx =1
(1/2)c[x^2]|(0->1) =1
c=2
(2)
P(-1<ξ<1/2)
=∫(0->1/2) 2x dx
=[x^2]|(0->1/2)
=1/4
(3)
E(ξ)
=∫(0->1) 2x^2 dx
=2/3
E(ξ^2)
=∫(0->1) 2x^3 dx
=1/2
D(ξ) = E(ξ^2)- [E(ξ)]^2 = 1/2 - 4/9 = 1/18
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