Question

麻烦解一下题目

急需，大神帮忙‘

Answer 1

(1)
E(X)
= (-1)(0.1) +(0)(0.2)+(1)(0.4)+(2)(0.3)
=-0.1 +0 +0.4 +0.6
=0.9
(2)
f(x)
=1+x , -1≤ x<0
=1-x , 0≤x <1
=0 , otherwise
E(X)
= ∫(-1->0) x(1+x) dx + ∫(0->1) x(1-x) dx
= [ (1/2)x^2 + (1/3)x^3 ]|(-1->0) + [ (1/2)x^2 - (1/3)x^3 ]|(0->1)
= -( 1/2 - 1/3) +( 1/2 -1/3)
=0
E(X^2)
= ∫(-1->0) x^2.(1+x) dx + ∫(0->1) x^2.(1-x) dx
= [ (1/3)x^3 + (1/4)x^4 ]|(-1->0) + [ (1/3)x^3 - (1/4)x^4 ]|(0->1)
= -( -1/3 + 1/4) +( 1/3 -1/4)
=1/6

D(X)=E(X^2)-[E(X)]^2 = 1/6